Boundedness of Mikhlin Operator in Variable Exponent Morrey Space

Document Type : Original Article

Author
Morteza Koozehgar Kalleji
Department of Mathematics, Faculty of Sciences, Arak University, Arak 38156-8-8349, Iran.
10.22034/maco.2.1.8
Abstract
S. G. Mikhlin proved the boundedness of the Fourier multiplier operator in the classical Lebesgue space if the multiplier function is a bounded function. In cite{MWW}, the authors obtained the same result of the classical Morrey space. In this paper, we prove that Mikhlin operator with bounded multiplier function is bounded operator on Morrey space with variable exponent which is containing the classical Lebesgue space with variable exponent and the classical Morrey space. 

Keywords

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Mathematical Analysis and Convex Optimization
Volume 2, Issue 1
June 2021
Pages 79-85