Article
Mathematics
Felix Voigtlaender
Summary: This paper investigates smoothness spaces in harmonic analysis and raises the question of whether there is an embedding between two such spaces. By defining the decomposition space norm and establishing verifiable conditions, sufficient criteria for the existence of an embedding are presented. Furthermore, it is proven that two decomposition spaces can only coincide if their ingredients are equivalent. The resulting embedding theory has made significant progress in practical applications.
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Mathematics, Applied
Dorothee D. Haroske, Susana D. Moura, Leszek Skrzypczak
Summary: This study investigates embeddings between generalised Besov-Morrey spaces Ns phi,p,q(Rd), proving both sufficient and necessary conditions for the embeddings. The embeddings of Besov-Morrey spaces into Lebesgue spaces Lr(Rd) are also discussed. The approach used in this study involves wavelet characterisation of spaces established for the Daubechies wavelets system.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Mathematics, Applied
Glenn Byrenheid, Janina Huebner, Markus Weimar
Summary: This paper focuses on the sparse approximation of functions with hybrid regularity borrowed from Yserentant's theory of solutions to electronic Schrodinger equations (2004) [42]. Hyperbolic wavelets are used to introduce new spaces of Besov-and Triebel-Lizorkin-type, specifically covering the energy norm approximation of functions with dominant mixed smoothness. Explicit adaptive and non-adaptive algorithms are derived, providing sharp dimension-independent rates of convergence.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2023)
Article
Mathematics
D. E. EDMUNDS, A. GOGATISHVILI, A. NEKVINDA
Summary: This article provides necessary and sufficient conditions for embedding variable exponent spaces and presents conditions for compact embedding of Sobolev spaces based on variable exponent spaces. The article also includes previous results as special cases.
STUDIA MATHEMATICA
(2023)
Article
Computer Science, Theory & Methods
Dorothee D. Haroske, Hans-Gerd Leopold, Leszek Skrzypczak
Summary: This article studies nuclear embeddings for function spaces of Besov and Triebel-Lizorkin type defined on quasi-bounded domains, and provides the first complete result on nuclearity in this context. Furthermore, the famous Tong result is generalized to general vector-valued sequence spaces.
JOURNAL OF COMPLEXITY
(2022)
Article
Mathematics, Applied
Beata Deregowska, Beata Gryszka, Karol Gryszka, Pawel Wojcik
Summary: This paper investigates semi-smooth points in spaces of continuous functions by providing a description in the context of C-0(T, E) and presenting necessary and sufficient conditions for semi-smoothness in the general case.
RESULTS IN MATHEMATICS
(2022)
Article
Mathematics
Jana Bjorn, Agnieszka Kalamajska
Summary: This article studies the compactness and boundedness of embeddings from Sobolev-type spaces on metric spaces into L-q spaces with respect to another measure. The Sobolev spaces considered can be of fractional order and some statements also allow non-doubling measures. The results are formulated in a general form, using sequences of covering families and local Poincare-type inequalities. Various Sobolev spaces are simultaneously treated, including the Newtonian, fractional Hajlasz, and Poincare-type spaces. For locally doubling measures, a self-improvement property for two weighted Poincare inequalities is proven.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Mathematics
D. E. Edmunds, J. Lang
Summary: The paper discusses the embedding of a first-order Sobolev space in a Lebesgue space on a bounded open set and provides an example where the embedding is not strictly singular. The same result is shown to hold when the open set is an infinite strip.
JOURNAL OF APPROXIMATION THEORY
(2023)
Article
Mathematics
Yoshihiro Mizuta, Takao Ohno, Tetsu Shimomura
Summary: The study focuses on the compact embedding properties of Sobolev spaces with two variable exponents, where the exponents satisfy certain conditions.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
(2022)
Article
Mathematics
S. Butler
Summary: This article investigates deficient topological measures on locally compact spaces, exploring properties such as positive, negative, and total variation, as well as finite additivity. It presents methods for generating new deficient topological measures and provides necessary and sufficient conditions for a deficient topological measure to be a topological measure or a measure. These results are crucial for further research on topological measures, deficient topological measures, and corresponding non-linear functionals on locally compact spaces.
MATHEMATISCHE NACHRICHTEN
(2021)
Article
Mathematics, Applied
Yu Zhou
Summary: This paragraph mainly discusses the properties and relationships on real Banach spaces, including embeddings, linear operators, isometric embeddings, etc.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Nihat Gokhan Gogus
Summary: In this paper, we prove that the projective limit of a certain class of Dirichlet-type spaces is isomorphic to the Bloch-type spaces B-alpha. We provide a complete characterization of bounded or compact embeddings of B-alpha into a family of Lebesgue spaces by the derivative operator. As an application, we prove precise necessary and sufficient criteria for boundedness/compactness of the generalized composition operators. The Dirichlet-type intermediate spaces constructed in this paper serve very useful.
ANNALS OF FUNCTIONAL ANALYSIS
(2022)
Article
Mathematics
Alireza Amini-Harandi, Ian Doust, Gavin Robertson
Summary: This paper explores the roundness and coroundness of Banach spaces, providing simple computations and explicit examples. Equivalent conditions for maximal roundness greater than 1 are given, and conclusions about non-trivial values in certain Orlicz spaces are drawn. Additionally, an explicit example of a 2-dimensional Banach space with non-equal maximal roundness to its dual is provided.
JOURNAL OF FUNCTIONAL ANALYSIS
(2021)
Article
Mathematics
O. V. Besov
Summary: We establish theorems concerning embeddings and compact embeddings of spaces of functions with positive smoothness defined on Holder domains in Lebesgue spaces in n-dimensional Euclidean space.
MATHEMATICAL NOTES
(2023)
Article
Mathematics, Applied
Merve Ilkhan, Evren Emrah Kara, Fuat Usta
Summary: This paper explores the necessary and sufficient conditions for compactness of a matrix operator between Banach spaces, as well as characterizing compact operators on Jordan totient sequence spaces. The concept of the Hausdorff measure of noncompactness plays a crucial role in both analyses.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)