O'Neil Inequality for Convolutions Associated with Gegenbauer Differential Operator and Some Applications
Year: 2020
Author: Vagif S. Guliyev, E.J. Ibrahimov, S.E. Ekincioglu, S. Ar. Jafarova
Journal of Mathematical Study, Vol. 53 (2020), Iss. 1 : pp. 90–124
Abstract
In this paper we prove an O'Neil inequality for the convolution operator ($G$-convolution) associated with the Gegenbauer differential operator $G_{\lambda}$. By using an O'Neil inequality for rearrangements we obtain a pointwise rearrangement estimate of the $G$-convolution. As an application, we obtain necessary and sufficient conditions on the parameters for the boundedness of the $G$-fractional maximal and $G$-fractional integral operators from the spaces $L_{p,\lambda}$ to $L_{q,\lambda }$ and from the spaces $L_{1,\lambda }$ to the weak spaces $WL_{p,\lambda}$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v53n1.20.05
Journal of Mathematical Study, Vol. 53 (2020), Iss. 1 : pp. 90–124
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: Gegenbauer differential operator $G$-convolution O'Neil inequality $G$-fractional integral $G$-fractional maximal function.