期刊
ANALYSIS AND APPLICATIONS
卷 21, 期 2, 页码 353-383出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219530522500038
关键词
Schrodinger; inverse square potential; variation operator; oscillation operator; maximal operator; Weyl fractional derivative
This paper investigates the semigroup of operators generated by the Friedrichs extension of the Schrodinger operator with the inverse square potential. Weighted L-p inequalities are established for operators associated with the Weyl fractional derivative. The range of suitable p values differs depending on the value of a.
By {T-t(a)}t>0 we denote the semigroup of operators generated by the Friedrichs extension of the Schrodinger operator with the inverse square potential L-a = -Delta + a/vertical bar x vertical bar(2) defined in C-c(infinity) (R-n\{0}). In this paper, we establish weighted L-p-inequalities for the maximal, variation, oscillation and jump operators associated with {t(alpha)partial derivative T-alpha(t)t(alpha)}t> o, where alpha >= 0 and partial derivative(alpha)(t) denotes the Weyl fractional derivative. The range of values p that works is different when a >= 0 and when -(n-2)(2)/4 < a < 0.
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