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Maximal Operator with Rough Kernel in Variable Musielak–Morrey–Orlicz type Spaces, Variable Herz Spaces and Grand Variable Lebesgue Spaces

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Abstract

In the frameworks of some non-standard function spaces (viz. Musielak–Orlicz spaces, generalized Orlicz–Morrey spaces, generalized variable Morrey spaces and variable Herz spaces) we prove the boundedness of the maximal operator with rough kernel. The results are new even for p constant.

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Authors and Affiliations

  1. Departamento de Matemáticas, Facultad de Ciencias, Pontificia Universidad Javeriana, Cra. 7 # 43-82, Bogotá, Colombia

    Humberto Rafeiro

  2. Departamento de Matemática, Universidade do Algarve, Campus de Gambelas, 8005-139, Faro, Portugal

    Stefan Samko

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  1. Humberto Rafeiro
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  2. Stefan Samko
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Correspondence to Humberto Rafeiro.

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Rafeiro, H., Samko, S. Maximal Operator with Rough Kernel in Variable Musielak–Morrey–Orlicz type Spaces, Variable Herz Spaces and Grand Variable Lebesgue Spaces. Integr. Equ. Oper. Theory 89, 111–124 (2017). https://doi.org/10.1007/s00020-017-2398-2

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  • DOI: https://doi.org/10.1007/s00020-017-2398-2

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