Necessary and sufficient condition for the boundedness of the Gegenbauer–Riesz potential on Morrey spaces

Vagif S. Guliyev

doi:10.1515/GMJ-2018-0022

Necessary and sufficient condition for the boundedness of the Gegenbauer–Riesz potential on Morrey spaces

Vagif S. Guliyev

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Abstract

In this paper, we study the Riesz potential (G-Riesz potential) generated by the Gegenbauer differential operator G_{\lambda}=(x^{2}-1)^{\frac{1}{2}-\lambda}\frac{d}{dx}(x^{2}-1)^{\lambda+% \frac{1}{2}}\frac{d}{dx},\quad x\in(1,\infty),\,\lambda\in\Bigl{(}0,\frac{1}{2% }\Bigr{)}. We prove that the G-Riesz potential {I_{G}^{\alpha}} , {0

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A. Scapellato, Some properties of integral operators on generalized Morrey spaces, AIP Conf. Proc. 1863 (2017), DOI 10.1063/1.4992662. Brought to you by | University of Sussex Library Authenticated Download Date | 3/30/18 11:12 AM