O'Neil Inequality for Convolutions Associated with Gegenbauer Differential Operator and some Applications

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Guliyev V. S., Ibrahimov E. J., Ekincioglu S. E., Jafarova S.

JOURNAL OF MATHEMATICAL STUDY, vol.53, no.1, pp.90-124, 2020 (ESCI, Scopus)

• Publication Type: Article / Article
• Volume: 53 Issue: 1
• Publication Date: 2020
• Doi Number: 10.4208/jms.v53n1.20.05
• Journal Name: JOURNAL OF MATHEMATICAL STUDY
• Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
• Page Numbers: pp.90-124
• Open Archive Collection: Article, Digital Heritage Collection
• Azerbaijan State University of Economics (UNEC) Affiliated: Yes

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,L-lambda to L-q,L-lambda and from the spaces L-1,L-lambda to the weak spaces WLp,lambda.