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Predual space and Calderón construction for grand weighted Morrey spaces, and some applications

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Abstract

We investigate duality and interpolation problems in two-weighted grand Morrey spaces. In particular, we discuss the predual space and Calderón construction for these spaces. Based on these and some known results, we establish complex interpolation for two-weighted grand Morrey spaces. The derived interpolation result enables us to show that the boundedness of a linear bounded operator in one-weighted Morrey space with Muckenhoupt weight implies its boundedness in one-weighted grand Morrey space with the same weight.

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Acknowledgements

The authors are grateful to the referees for valuable remarks and suggestions which improved the manuscript.

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Authors and Affiliations

  1. A. Razmade Mathematical Institute of I. Javakhishvili Tbilisi State University, 2 Merab Aleksidze II Lane, 0193, Tbilisi, Georgia

    Alexander Meskhi

  2. Kutaisi International University, 5th Lane, K Building, 4600, Kutaisi, Georgia

    Alexander Meskhi

  3. College of Sciences, Department of Mathematical Sciences, United Arab Emirates University, PO Box 15551, Al Ain, United Arab Emirates

    Humberto Rafeiro

  4. Department of Mathematics, Faculty of Informatics and Control Systems, Georgian Technical University, 77, Kostava St., Tbilisi, Georgia

    Tsira Tsanava

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  1. Alexander Meskhi
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  2. Humberto Rafeiro
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  3. Tsira Tsanava
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Correspondence to Humberto Rafeiro.

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The authors do not have any conflicts of interest to disclose. H.R. was supported by a UPAR Grant of United Arab Emirates University, UAE, via Grant G00004572.

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Meskhi, A., Rafeiro, H. & Tsanava, T. Predual space and Calderón construction for grand weighted Morrey spaces, and some applications. Bol. Soc. Mat. Mex. 30, 47 (2024). https://doi.org/10.1007/s40590-024-00607-6

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