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2020 Boundedness of weighted iterated Hardy-type operators involving suprema from weighted Lebesgue spaces into weighted Cesàro function spaces
Nevin Bilgiçli, Rza Mustafayev
Real Anal. Exchange 45(2): 339-374 (2020). DOI: 10.14321/realanalexch.45.2.0339

Abstract

The boundedness of the weighted iterated Hardy-type operators \(T_{u,b}\) and \(T_{u,b}^*\) involving suprema from weighted Lebesgue space \(L_p(v)\) into weighted Cesàro function spaces \({\operatorname{Ces}}_{q}(w,a)\) are characterized. These results allow us to obtain the characterization of the boundedness of the supremal operator \(R_u\) from \(L^p(v)\) into \({\operatorname{Ces}}_{q}(w,a)\) on the cone of monotone non-increasing functions. For the convenience of the reader, we formulate the statement on the boundedness of the weighted Hardy operator \(P_{u,b }\) from \(L^p(v)\) into \({\operatorname{Ces}}_{q}(w,a)\) on the cone of monotone non-increasing functions. Under additional condition on \(u\) and \(b\), we are able to characterize the boundedness of weighted iterated Hardy-type operator \(T_{u,b}\) involving suprema from \(L^p(v)\) into \({\operatorname{Ces}}_q(w,a)\) on the cone of monotone non-increasing functions. At the end of the paper, as an application of obtained results, we calculate the norm of the fractional maximal function \(M_{\gamma}\) from \(\Lambda^p(v)\) into \(\Gamma^q(w)\).

Citation

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Nevin Bilgiçli. Rza Mustafayev. "Boundedness of weighted iterated Hardy-type operators involving suprema from weighted Lebesgue spaces into weighted Cesàro function spaces." Real Anal. Exchange 45 (2) 339 - 374, 2020. https://doi.org/10.14321/realanalexch.45.2.0339

Information

Published: 2020
First available in Project Euclid: 30 June 2020

zbMATH: 07229051
Digital Object Identifier: 10.14321/realanalexch.45.2.0339

Subjects:
Primary: 26D10, 42B25, 42B35, 46E30

Rights: Copyright © 2020 Michigan State University Press

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Vol.45 • No. 2 • 2020
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