Calderón Operator on Local Morrey Spaces with Variable Exponents

In this paper, we establish the boundedness of the Calderón operator on local Morrey spaces with variable exponents. We obtain our result by extending the extrapolation theory of Rubio de Francia to the local Morrey spaces with variable exponents. The exponent functions of the local Morrey spaces wi...

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Autor principal:	Kwok-Pun Ho
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Calderón operator Hardy’s inequality variable Lebesgue space local Morrey space local block space extrapolation Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/f7800fe6192d4b578fc4af56efbb15a7
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id	oai:doaj.org-article:f7800fe6192d4b578fc4af56efbb15a7
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spelling	oai:doaj.org-article:f7800fe6192d4b578fc4af56efbb15a72021-11-25T18:17:45ZCalderón Operator on Local Morrey Spaces with Variable Exponents10.3390/math92229772227-7390https://doaj.org/article/f7800fe6192d4b578fc4af56efbb15a72021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2977https://doaj.org/toc/2227-7390In this paper, we establish the boundedness of the Calderón operator on local Morrey spaces with variable exponents. We obtain our result by extending the extrapolation theory of Rubio de Francia to the local Morrey spaces with variable exponents. The exponent functions of the local Morrey spaces with the exponent functions are only required to satisfy the log-Hölder continuity assumption at the origin and infinity only. As special cases of the main result, we have Hardy’s inequalities, the Hilbert inequalities and the boundedness of the Riemann–Liouville and Weyl averaging operators on local Morrey spaces with variable exponents.Kwok-Pun HoMDPI AGarticleCalderón operatorHardy’s inequalityvariable Lebesgue spacelocal Morrey spacelocal block spaceextrapolationMathematicsQA1-939ENMathematics, Vol 9, Iss 2977, p 2977 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Calderón operator Hardy’s inequality variable Lebesgue space local Morrey space local block space extrapolation Mathematics QA1-939
spellingShingle	Calderón operator Hardy’s inequality variable Lebesgue space local Morrey space local block space extrapolation Mathematics QA1-939 Kwok-Pun Ho Calderón Operator on Local Morrey Spaces with Variable Exponents
description	In this paper, we establish the boundedness of the Calderón operator on local Morrey spaces with variable exponents. We obtain our result by extending the extrapolation theory of Rubio de Francia to the local Morrey spaces with variable exponents. The exponent functions of the local Morrey spaces with the exponent functions are only required to satisfy the log-Hölder continuity assumption at the origin and infinity only. As special cases of the main result, we have Hardy’s inequalities, the Hilbert inequalities and the boundedness of the Riemann–Liouville and Weyl averaging operators on local Morrey spaces with variable exponents.
format	article
author	Kwok-Pun Ho
author_facet	Kwok-Pun Ho
author_sort	Kwok-Pun Ho
title	Calderón Operator on Local Morrey Spaces with Variable Exponents
title_short	Calderón Operator on Local Morrey Spaces with Variable Exponents
title_full	Calderón Operator on Local Morrey Spaces with Variable Exponents
title_fullStr	Calderón Operator on Local Morrey Spaces with Variable Exponents
title_full_unstemmed	Calderón Operator on Local Morrey Spaces with Variable Exponents
title_sort	calderón operator on local morrey spaces with variable exponents
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/f7800fe6192d4b578fc4af56efbb15a7
work_keys_str_mv	AT kwokpunho calderonoperatoronlocalmorreyspaceswithvariableexponents
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Calderón Operator on Local Morrey Spaces with Variable Exponents

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