Singular integrals and potentials in grand Lebesgue spaces

Vakhtang Kokilashvili; Alexander Meskhi; Humberto Rafeiro; Stefan Samko

doi:10.1007/978-3-319-21018-6_4

Singular integrals and potentials in grand Lebesgue spaces

Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko

Research output: Chapter in Book/Report/Conference proceeding › Chapter

9 Citations (Scopus)

Abstract

This chapter deals with mapping properties of maximal, singular integral, and potential operators in weighted generalized grand Lebesgue spaces. Weak and strong type weighted inequalities criteria for these operators (including similar integral transform with product kernels) are established. Single-weight criteria in grand Lebesgue spaces for the Hardy and Riemann-Liouville operators on the cone of non-increasing functions are derived.

Original language	English
Title of host publication	Operator Theory
Subtitle of host publication	Advances and Applications
Publisher	Springer International Publishing
Pages	741-849
Number of pages	109
DOIs	https://doi.org/10.1007/978-3-319-21018-6_4
Publication status	Published - 2016
Externally published	Yes

Publication series

Name	Operator Theory: Advances and Applications
Volume	249
ISSN (Print)	0255-0156
ISSN (Electronic)	2296-4878

ASJC Scopus subject areas

Analysis

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10.1007/978-3-319-21018-6_4

Cite this

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AU - Meskhi, Alexander

AU - Rafeiro, Humberto

AU - Samko, Stefan

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AB - This chapter deals with mapping properties of maximal, singular integral, and potential operators in weighted generalized grand Lebesgue spaces. Weak and strong type weighted inequalities criteria for these operators (including similar integral transform with product kernels) are established. Single-weight criteria in grand Lebesgue spaces for the Hardy and Riemann-Liouville operators on the cone of non-increasing functions are derived.

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Singular integrals and potentials in grand Lebesgue spaces

Abstract

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