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 Gλ. 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 Lp,λ to Lq,λ and from the spaces L1,λ to the weak spaces WLp,λ.
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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.
Author Details
Vagif S. Guliyev Email
E.J. Ibrahimov Email
S.E. Ekincioglu Email
S. Ar. Jafarova Email
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Weak and strong type inequalities criteria for fractional maximal functions and fractional integrals associated with Gegenbauer differential operator
Kokilashvili, Vakhtang
Ibrahimov, Elman J.
Georgian Mathematical Journal, Vol. 30 (2023), Iss. 5 P.745
https://doi.org/10.1515/gmj-2023-2031 [Citations: 1]