$B-$ Riezs potential in $B-$ local Morrey-Lorentz spaces

Year 2024, Volume: 73 Issue: 2, 437 - 449, 21.06.2024

Esra Kaya , Canay Aykol

https://doi.org/10.31801/cfsuasmas.1359782

Abstract

In this paper, the Riesz potential (B−Riesz potential) which are generated by the Laplace-Bessel differential operator will be studied. We obtain the necessary and sufficient conditions for the boundedness of the B−Riesz potential $I_{\gamma }^{\alpha }$ in the B-local Morrey-Lorentz spaces $M_{p,q,\lambda,\gamma }^{loc}(\mathbb{R}_{k,+}^{n})$ with the use of the rearrangement inequalities and boundedness of the Hardy operators $H_{\upsilon }^{\beta }$ and $\mathcal{H}_{\upsilon}^{\beta }$ with power weights.

Keywords

Morrey spaces, Lorentz spaces, local Morrey-Lorentz spaces, Riesz potential

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