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Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators

  • Ferit Gürbüz ORCID logo EMAIL logo , Shenghu Ding , Huili Han and Pinhong Long
Published/Copyright: October 28, 2020

Abstract

In this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.

2010 Mathematics Subject Classification: Primary 42B20; Secondary 42B35; 46E30

Corresponding author: Ferit Gürbüz, Faculty of Education, Department of Mathematics Education, Hakkari University, Hakkari 30000, Turkey, E-mail:

Funding source: Hakkari University Scientific Research Project

Award Identifier / Grant number: FM18BAP1

Funding source: Institution of Higher Education Scientific Research Project in Ningxia

Award Identifier / Grant number: NGY2017011

Award Identifier / Grant number: 11461053

Award Identifier / Grant number: 11762016

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This work is funded by Hakkari University Scientific Research Project (Grant no. FM18BAP1) under the research project “Some estimates for rough Riesz type potential operator with variable order and rough fractional maximal operator with variable order both on generalized variable exponent Morrey spaces and vanishing generalized variable exponent Morrey spaces”, Institution of Higher Education Scientific Research Project in Ningxia (Grant no. NGY2017011) and Natural Science Foundation of China (Grant nos. 11461053 and 11762016).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2019-06-24
Accepted: 2020-09-25
Published Online: 2020-10-28
Published in Print: 2021-10-26

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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