Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 15 (2020), 295 -- 313

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This work is licensed under a Creative Commons Attribution 4.0 International License.

BOUNDEDNESS OF LITTLEWOOD-PALEY OPERATORS WITH VARIABLE KERNEL ON THE WEIGHTED HERZ-MORREY SPACES WITH VARIABLE EXPONENT

Afif Abdalmonem, Omer Abdalrhman and Shuangping Tao

Abstract. Let Ω∈L∞(ℝn)×L2(Sn-1) be a homogeneous function of degree zero. In this article, we obtain some boundedness of the parameterized Littlewood-Paley operators with variable kernels on weighted Herz-Morrey spaces with variable exponent. As a supplement, the boundedness of fractional integral operators with variable kernel is also obtained on these spaces.

2020 Mathematics Subject Classification: 43A15; 43A85
Keywords: Parameterized Littlewood-Paley operators; variable kernel; weighted Herz space; Muckenhoupt weight; variable exponent.

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Afif Abdalmonem
Faculty of Science, University of Dalanj, Dalanj, Sudan.
e-mail:afeefy86@gmail.com

Omer Abdalrhman
College of Education, Shendi University, Shendi, Sudan.
e-mail: humoora@gmail.com

Shuangping Tao
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China.
e-mail: taosp@nwnu.edu.cn

http://www.utgjiu.ro/math/sma