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Ricerche di Matematica

, Volume 68, Issue 2, pp 661–677 | Cite as

Dilation operators and integral operators on amalgam space \((L_{p},l_{q})\)

  • Kwok-Pun HoEmail author
Article

Abstract

This paper establishes the Hardy–Littlewood–Pólya inequalities, the Hardy inequalities and the Hilbert inequalities on amalgam spaces. Moreover, it also gives the mapping properties of the Mellin convolutions, the Hadamard fractional integrals and the Hausdorff operators on amalgam spaces. We establish these properties by some estimates for the operator norms of the dilation operators on amalgam spaces.

Keywords

Amalgam spaces Integral operator Hardy inequality Hilbert inequality Hadamard fractional integral Mellin convolution Hausdorff operator 

Mathematics Subject Classification

26D10 26D15 42B35 44A05 46E30 

Notes

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Copyright information

© Università degli Studi di Napoli "Federico II" 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Information TechnologyThe Education University of Hong KongTai PoChina

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