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Maximal Operator in Variable Stummel Spaces

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Abstract

We prove that variable exponent Morrey spaces are closely embedded between variable exponent Stummel spaces. We also study the boundedness of the maximal operator in variable exponent Stummel spaces as well as in vanishing variable exponent Stummel spaces.

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Acknowledgements

We are grateful to the anonymous referees for their careful reading and useful comments and suggestions. The research of A. Almeida was partially supported by the Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), references UIDB/04106/2020 and UIDP/04106/2020. The research of H. Rafeiro was supported by a Start-up Grant of United Arab Emirates University, Al Ain, United Arab Emirates via Grant No. G00002994.

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Authors and Affiliations

  1. Department of Mathematics, Center for R &D in Mathematics and Applications, University of Aveiro, 3810-193, Aveiro, Portugal

    Alexandre Almeida

  2. Department of Mathematical Sciences, College of Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, Abu Dhabi, UAE

    Humberto Rafeiro

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  1. Alexandre Almeida
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  2. Humberto Rafeiro
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Correspondence to Humberto Rafeiro.

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Communicated by Alexey Karapetyants.

Dedicated to the 80th anniversary of Professor Stefan Samko.

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Almeida, A., Rafeiro, H. Maximal Operator in Variable Stummel Spaces. J Fourier Anal Appl 28, 50 (2022). https://doi.org/10.1007/s00041-022-09940-8

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  • DOI: https://doi.org/10.1007/s00041-022-09940-8

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