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Extrapolation in weighted classical and grand Lorentz spaces. Application to the boundedness of integral operators

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Abstract

We establish weighted extrapolation theorems in classical and grand Lorentz spaces. As a consequence we have the weighted boundedness of operators of Harmonic Analysis in grand Lorentz spaces. We treat both cases: diagonal and off-diagonal ones.

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Acknowledgements

The authors are grateful to the referee for helpful remarks. The work was supported by the Shota Rustaveli National Science Foundation of Georgia (Project No. DI 18-118).

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Authors and Affiliations

  1. Department of Mathematical Analysis, A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, Tamarashvili Str. 6, 0177, Tbilisi, Georgia

    Vakhtang Kokilashvili & Alexander Meskhi

  2. Department of Mathematics, Faculty of Informatics and Control Systems, Georgian Technical University, 77, Kostava St., 0175, Tbilisi, Georgia

    Alexander Meskhi

Authors
  1. Vakhtang Kokilashvili
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  2. Alexander Meskhi
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Correspondence to Alexander Meskhi.

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Communicated by Jörg Eschmeier.

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Kokilashvili, V., Meskhi, A. Extrapolation in weighted classical and grand Lorentz spaces. Application to the boundedness of integral operators. Banach J. Math. Anal. 14, 1111–1142 (2020). https://doi.org/10.1007/s43037-020-00054-1

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  • DOI: https://doi.org/10.1007/s43037-020-00054-1

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