TY - JOUR
T1 - O'Neil Inequality for Convolutions Associated with Gegenbauer Differential Operator and Some Applications
AU - Guliyev , Vagif S.
AU - Ibrahimov , E.J.
AU - Ekincioglu , S.E.
AU - Jafarova , S. Ar.
JO - Journal of Mathematical Study
VL - 1
SP - 90
EP - 124
PY - 2020
DA - 2020/03
SN - 53
DO - http://doi.org/10.4208/jms.v53n1.20.05
UR - https://global-sci.org/intro/article_detail/jms/15209.html
KW - Gegenbauer differential operator, $G$-convolution, O'Neil inequality, $G$-fractional integral, $G$-fractional maximal function.
AB - <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>