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Calderón Operator on Local Morrey Spaces with Variable Exponents

Author

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  • Kwok-Pun Ho

    (Department of Mathematics and Information Technology, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, Hong Kong, China)

Abstract

In this paper, we establish the boundedness of the Calderón operator on local Morrey spaces with variable exponents. We obtain our result by extending the extrapolation theory of Rubio de Francia to the local Morrey spaces with variable exponents. The exponent functions of the local Morrey spaces with the exponent functions are only required to satisfy the log-Hölder continuity assumption at the origin and infinity only. As special cases of the main result, we have Hardy’s inequalities, the Hilbert inequalities and the boundedness of the Riemann–Liouville and Weyl averaging operators on local Morrey spaces with variable exponents.

Suggested Citation

  • Kwok-Pun Ho, 2021. "Calderón Operator on Local Morrey Spaces with Variable Exponents," Mathematics, MDPI, vol. 9(22), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2977-:d:685050
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