In this paper we consider global Morrey spaces with variable exponents p(.), θ(.), where is an unbounded set. The questions of boundedness of the singular integral operator and its commutator in these spaces are investigated. We give the conditions for the variable exponent and for the functions ( (.), (.)) under which the singular integral operator will be bounded from to . The same conditions for the boundedness of the commutator of the singular integral operator in these spaces are obtained.. In the case when the exponents are constant numbers, the questions of boundedness of the singular integral operator and its commutator in global spaces were previously studied by other authors. There are also well-known results on the boundedness of a singular integral operator in the global Morrey-type spaces with variable exponents when the set is bounded.
The CALDERON-ZIGMUND SINGULAR INTEGRAL IN THE MORREY-TYPE SPACES WITH VARIABLE EXPONENTS
Published June 2022
Abstract
Language
Eng
Keywords
singular integral operator
commutator
boundedness
Morrey-type spaces
variable exponents
unbounded set
Holder inequality
How to Cite
[1]
Bokayev, .N. and Onerbek, Z. 2022. The CALDERON-ZIGMUND SINGULAR INTEGRAL IN THE MORREY-TYPE SPACES WITH VARIABLE EXPONENTS. Bulletin of the Abai KazNPU, the series of "Physical and Mathematical Sciences". 78, 2 (Jun. 2022), 7–13. DOI:https://doi.org/10.51889/2022-2.1728-7901.01.