@Article{JMS-53-1,
author = {Vagif, S., Guliyev and Ibrahimov, E.J. and S.E., Ekincioglu and S., Jafarova, Ar.},
title = {O'Neil Inequality for Convolutions Associated with Gegenbauer Differential Operator and Some Applications},
journal = {Journal of Mathematical Study},
year = {2020},
volume = {53},
number = {1},
pages = {90--124},
abstract = {<p style="text-align: justify;">In this paper we prove an O&#39;Neil inequality for the convolution operator ($G$-convolution) associated with the Gegenbauer differential operator $G_{\lambda}$. By using an O&#39;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 $WL_{p,\lambda}$.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v53n1.20.05},
url = {https://global-sci.com/article/87692/oneil-inequality-for-convolutions-associated-with-gegenbauer-differential-operator-and-some-applications}
}