Article
Mathematics
Ebrahim Abbasi, Xiangling Zhu
Summary: This paper presents characterizations for the boundedness, compactness, and essential norm of a class of product-type operators T-u,v,phi(n) from the Bloch space and little Bloch space into Zygmund-type spaces.
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics
Jose Angel Pelaez, Jouni Rattya, Fanglei Wu
Summary: This article examines the problem of describing analytic functions g on the unit disc that make the integral operator T-g(f)(z) = ?(z)(0) f (?)g'(?)d? bounded or compact when mapping from a Banach space or complete metric space X of analytic functions to the Hardy space H-8. This problem remains unresolved in many cases. The article provides a description of the boundedness and compactness of T-g when acting from a weighted Dirichlet space D-?(p), induced by an upper doubling weight ?, to H-8 for analytic functions g with non-negative Maclaurin coefficients. Additionally, the article characterizes the upper doubling weights for which T-g : D-?(p) ? H-8 is bounded or compact only if g is constant.
MATHEMATISCHE ZEITSCHRIFT
(2023)
Article
Mathematics, Applied
Stevo Stevic
Summary: This article provides formulas for the norm and essential norm of a product of composition and integral operators in Bloch-type spaces of analytic functions on the unit ball. The formulas are expressed in terms of given symbols and weights.
Article
Mathematics, Applied
Stevo Stevic
Summary: In this paper, we calculate the norm and essential norm of an integral-type operator from the logarithmic Bloch space and the little logarithmic Bloch space to Bloch-type spaces. We show that there is a one-parameter class of equivalent norms on the logarithmic Bloch space for which the norms can be calculated.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics
Maofa Wang, Shuming Wang
Summary: The text discusses the Banach space of holomorphic functions on the open unit disk in the complex plane, as well as the boundedness characterizations, norm estimates, and essential norm estimates of weighted composition operators. It also covers the compactness characterization of the operators, extending various known results in the literature.
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Zhitao Guo, Linlin Liu
Summary: This article characterizes the boundedness and compactness of a class of product-type operators from Hardy spaces to Bloch-type space and Zygmund-type space. The norm of these operators is also estimated.
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
(2022)
Article
Mathematics, Applied
Zhitao Guo, Jianyong Mu
Summary: This paper investigates the boundedness, essential norm and compactness of a generalized operator under the conditions of analytic functions and analytic self-map.
Article
Mathematics
Shaolin Chen, Hidetaka Hamada, Jian-Feng Zhu
Summary: The main purpose of this paper is to discuss Hardy type spaces, Bloch type spaces, and composition operators of complex-valued harmonic functions. It first establishes a sharp estimate for the Lipschitz continuity of complex-valued harmonic functions in Bloch type spaces, providing an answer to an open problem. Several classes of composition operators on Bloch and Hardy type spaces are then investigated, improving and extending previous known results.
MATHEMATISCHE ZEITSCHRIFT
(2022)
Article
Mathematics
Nanhui Hu
Summary: The boundedness, compactness, and the essential norm of weighted composition operators from derivative Hardy spaces into n-th weighted-type spaces are explored in this paper.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Hidetaka Hamada, Tatsuhiro Honda
Summary: In this paper, we investigate the composition operator C-phi between Bloch-type spaces and provide necessary conditions for its boundedness and compactness.
COMPLEX ANALYSIS AND OPERATOR THEORY
(2022)
Article
Mathematics, Applied
Xiangling Zhu, Qinghua Hu, Dan Qu
Summary: This paper provides characterizations for the boundedness, compactness, and essential norm of Stevic-Sharma-type operators called polynomial differentiation composition operators from Besov-type spaces into Bloch-type spaces on the unit disk.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Songxiao Li, Jizhen Zhou
Summary: In this paper, we characterize the boundedness and compactness of the Hankel operator H-μ from Bloch type spaces to BMOA and the Bloch space. Moreover, we obtain the essential norm of H-μ from B-α to B and BMOA.
Article
Mathematics
Xiangxing Tao, Yuan Zeng, Xiao Yu
Summary: This paper investigates the boundedness and compactness of the commutator [b, T-omega] generated by a symbol function b on the Lorentz space L-p,L-r (X), as well as the omega-type Calderon-Zygmund operator T-omega. The results hold for any p in the range (1, infinity) and r in the range [1, infinity).
ACTA MATHEMATICA SCIENTIA
(2023)
Article
Mathematics, Applied
Alejandro Miralles
Summary: This article studies the boundedness of composition operators on B(B-E), which are defined on the open unit ball B-E and involve Bloch functions.
BANACH JOURNAL OF MATHEMATICAL ANALYSIS
(2023)
Article
Mathematics
Xiangling Zhu
Summary: This paper introduces a family of Zygmund-type spaces called Dirichlet-Zygmund-type spaces and investigates the boundedness, compactness, and essential norm of weighted composition operators from Dirichlet-Zygmund-type spaces into Stevic-type spaces.
GEORGIAN MATHEMATICAL JOURNAL
(2023)
Article
Mathematics, Applied
Stevo Stevic, A. El-Sayed Ahmed, Bratislav Iricanin, Witold Kosmala
Summary: By using a comparison method and difference inequalities, we prove that a certain class of higher order difference equations with specific conditions has unbounded solutions, serving as counterexamples for the boundedness character of solutions to difference equations.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Stevo Stevic
Summary: This paper demonstrates that a recursive relation for finding square roots can be naturally derived from an iterative process and can be solved in closed form, providing an elegant explanation for some existing literature. Additionally, a new class of recursive relations for finding square roots, which can also be solved in closed form, is introduced, significantly expanding and unifying the field.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Mathematics, Applied
Stevo Stevic
Summary: In this paper, we present several classes of nonlinear difference equations that can be solved in closed form. These equations can be obtained from known iteration processes, and we also provide generalizations for some of them by introducing construction methods. We further conduct various analyses and offer comments on the difference equations and iteration processes.
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Stevo Stevic
Summary: This paper presents generalizations of results on the integer parts of the reciprocal remainders of the Zeta function and provides a short and elegant proof for the integer parts of the reciprocal remainders of the series Zeta(3). It also includes historical and theoretical remarks, analyses, and connections with the theory of linear difference equations with constant coefficients.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Stevo Stevic
Summary: In this paper, we calculate the norms of several specific operators, mostly integral-type operators between weighted-type spaces of continuous functions on different domains. Additionally, we determine the norm of an integral-type operator on certain subspaces of the weighted Lebesgue spaces.
Article
Mathematics, Applied
Stevo Stevic
Summary: This study characterizes the boundedness and compactness of a new class of linear operators from the weighted Bergman space to the weighted-type spaces on the unit ball.
Article
Mathematics, Applied
Stevo Stevic, Bratislav Iricanin, Witold Kosmala
Summary: This paper provides a detailed analysis of a class of nonlinear fourth-order difference equations. It studies the case where the parameters and initial values are positive real numbers and gives explanations and remarks related to the results and claims. It also addresses issues with some of the claims by providing counterexamples and compares the results with previous findings in the literature. Additionally, a global convergence result is presented.
ACTA APPLICANDAE MATHEMATICAE
(2023)
Article
Mathematics, Applied
Zheng Zhou, Bing Tan, Songxiao Li
Summary: This paper introduces two adaptive inertial iterative schemes for finding solutions of the split variational inclusion problem in Hilbert spaces, using the Meir-Keeler contraction method and the Mann-type method. The strong convergence of the suggested algorithms is guaranteed by a new stepsize criterion that does not require calculation of the bounded linear operator norm. Numerical experiments and applications in signal recovery problems are provided to demonstrate the efficiency of the proposed algorithms.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Stevo Stevic
Summary: This article provides formulas for the norm and essential norm of a product of composition and integral operators in Bloch-type spaces of analytic functions on the unit ball. The formulas are expressed in terms of given symbols and weights.
Article
Mathematics, Applied
Stevo Stevic, Bratislav Iricanin, Witold Kosmala
Summary: This article presents closed-form formulas for the general solution to a family of difference equations, considering conditions on initial values and parameters. It also extends some closed-form formulas for special cases of the difference equation to the general cases. Additionally, the article discusses the local and global stability of equilibrium points and the boundedness of positive solutions, providing comments and results related to these statements.
Article
Mathematics, Applied
Stevo Stevic, Durhasan Turgut Tollu
Summary: We consider a two-dimensional nonlinear system of difference equations with given delays and parameters, and find its general solution in detail.
Article
Mathematics, Applied
Stevo Stevic
Summary: We provide theoretical explanations for obtaining closed-form formulas and representations of general solutions for four special cases of a class of nonlinear second-order difference equations. We also propose an extension of this class of equations that can be solved in closed form, analyze the long-term behavior of the solutions, and present some convergence results.
Article
Mathematics, Applied
Stevo Stevic, Sei-ichiro Ueki
Summary: This paper investigates the boundedness, compactness, and estimates the essential norm of a polynomial differentiation composition operator from the Hardy space Hp to the weighted-type spaces of holomorphic functions on the unit ball.
JOURNAL OF MATHEMATICAL INEQUALITIES
(2023)
Article
Mathematics, Applied
Stevo Stevic
Summary: This paper investigates the polynomial differentiation composition operator and provides necessary and sufficient conditions for the boundedness and compactness of the operator from the logarithmic Bloch spaces to weighted-type spaces of holomorphic functions on B.
JOURNAL OF MATHEMATICAL INEQUALITIES
(2022)
Article
Mathematics, Applied
Lian Hu, Songxiao Li, Rong Yang
Summary: In this paper, we study the properties of 2-complex symmetric composition operators with the conjugation J in the Hardy space H-2, and provide the necessary and sufficient conditions for the composition operator to be 2-complex symmetric with J when the corresponding map is an automorphism or linear fractional self-map of D.
Article
Mathematics, Applied
Geunsu Choi, Mingu Jung, Sun Kwang Kim, Miguel Martin
Summary: This paper studies weak-star quasi norm attaining operators and proves that the set of such operators is dense in the space of bounded linear operators regardless of the choice of Banach spaces. It is also shown that weak-star quasi norm attaining operators have distinct properties from other types of norm attaining operators, although they may share some equivalent properties under certain conditions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maria Lorente, Francisco J. Martin-Reyes, Israel P. Rivera-Rios
Summary: In this paper, we provide quantitative one-sided estimates that recover the dependences in the classical setting. We estimate the one-sided maximal function in Lorentz spaces and demonstrate the applicability of the conjugation method for commutators in this context.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Fernando Cobos, Luz M. Fernandez-Cabrera
Summary: We provide a necessary and sufficient condition for the weak compactness of bilinear operators interpolated using the real method. However, this characterization does not hold for interpolated operators using the complex method.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ovgue Gurel Yilmaz, Sofiya Ostrovska, Mehmet Turan
Summary: The Lupas q-analogue Rn,q, the first q-version of the Bernstein polynomials, was originally proposed by A. Lupas in 1987 but gained popularity 20 years later when q-analogues of classical operators in approximation theory became a focus of intensive research. This work investigates the continuity of operators Rn,q with respect to the parameter q in both the strong operator topology and the uniform operator topology, considering both fixed and infinite n.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
M. Agranovsky, A. Koldobsky, D. Ryabogin, V. Yaskin
Summary: This article modifies the concept of polynomial integrability for even dimensions and proves that ellipsoids are the only convex infinitely smooth bodies satisfying this property.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Abel Komalovics, Lajos Molnar
Summary: In this paper, a parametric family of two-variable maps on positive cones of C*-algebras is defined and studied from various perspectives. The square roots of the values of these maps under a faithful tracial positive linear functional are considered as a family of potential distance measures. The study explores the problem of well-definedness and whether these distance measures are true metrics, and also provides some related trace characterizations. Several difficult open questions are formulated.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Frederic Bayart
Summary: The passage describes the construction of an operator on a separable Hilbert space that is 5-hypercyclic for all δ in the range (ε, 1) and is not 5-hypercyclic for all δ in the range (0, ε).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Helene Frankowska, Nikolai P. Osmolovskii
Summary: This paper investigates second-order optimality conditions for the minimization problem of a C2 function f on a general set K in a Banach space X. Both necessary and sufficient conditions are discussed, with the sufficiency condition requiring additional assumptions. The paper demonstrates the validity of these assumptions for the case when the set K is an intersection of sets described by smooth inequalities and equalities, such as in mathematical programming problems. The novelty of the approach lies in the arbitrary nature of the set K and the straightforward proofs.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ole Fredrik Brevig, Kristian Seip
Summary: This paper studies the Hankel operator on the Hardy space and discusses its minimal and maximal norms, as well as the relationship between the maximal norm and the properties of the function.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Alexander Meskhi
Summary: Rubio de Francia's extrapolation theorem is established for new weighted grand Morrey spaces Mp),lambda,theta w (X) with weights w beyond the Muckenhoupt Ap classes. This result implies the one-weight inequality for operators of Harmonic Analysis in these spaces for appropriate weights. The necessary conditions for the boundedness of the Hardy-Littlewood maximal operator and the Hilbert transform in these spaces are also obtained. Some structural properties of new weighted grand Morrey spaces are investigated. Problems are studied in the case when operators and spaces are defined on spaces of homogeneous type.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maud Szusterman
Summary: In this work, the necessary conditions on the structure of the boundary of a convex body K to satisfy all inequalities are investigated. A new solution for the 3-dimensional case is obtained in particular.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Rami Ayoush, Michal Wojciechowski
Summary: In this article, lower bounds for the lower Hausdorff dimension of finite measures are provided under certain restrictions on their quaternionic spherical harmonics expansions. This estimate is analogous to a result previously obtained by the authors for complex spheres.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
F. G. Abdullayev, V. V. Savchuk
Summary: This paper investigates the convergence and theorem proof of the Takenaka-Malmquist system and Fejer-type operator on the unit circle, and provides relevant results on the class of holomorphic functions representable by Cauchy-type integrals with bounded densities.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Sofiya Ostrovska, Mikhail I. Ostrovskii
Summary: This work aims to establish new results on the structure of transportation cost spaces. The main outcome of this paper states that if a metric space X contains an isometric copy of L1 in its transportation cost space, then it also contains a 1-complemented isometric copy of $1.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Pilar Rueda, Enrique A. Sanchez Perez
Summary: We prove a factorization theorem for Lipschitz operators acting on certain subsets of metric spaces of measurable functions and with values on general metric spaces. Our results show how a Lipschitz operator can be extended to a subset of other metric space of measurable functions that satisfies the following optimality condition: it is the biggest metric space, formed by measurable functions, to which the operator can be extended preserving the Lipschitz constant. Also, we demonstrate the coarsest metric that can be given for a metric space in which an order bounded lattice-valued-Lipschitz map is defined, and provide concrete examples involving the relevant space L0(mu).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
