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

Authors : Esra Kaya, Canay Aykol

Pages : 437-449

Doi:10.31801/cfsuasmas.1359782

View : 43 | Download : 55

Publication Date : 2024-06-21

Article Type : Research Paper

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