A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces

In this paper, we consider the maximal operator related to the Laplace-Bessel differential operator (BB-maximal operator) on Lp(⋅),γ(Rk,+n){L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces. We will give a necessary condition for the boundedness of the BB-m...

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Autor principal:	Kaya Esra
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	b-maximal operator generalized translation operator singular integrals variable exponent lebesgue spaces 42a50 42b25 42b35 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/4748c6e8a41244f69bf3938d7df26ba5
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spelling	oai:doaj.org-article:4748c6e8a41244f69bf3938d7df26ba52021-12-05T14:10:53ZA note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces2391-545510.1515/math-2021-0041https://doaj.org/article/4748c6e8a41244f69bf3938d7df26ba52021-05-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0041https://doaj.org/toc/2391-5455In this paper, we consider the maximal operator related to the Laplace-Bessel differential operator (BB-maximal operator) on Lp(⋅),γ(Rk,+n){L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces. We will give a necessary condition for the boundedness of the BB-maximal operator on variable exponent Lebesgue spaces. Moreover, we will obtain that the BB-maximal operator is not bounded on Lp(⋅),γ(Rk,+n){L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces in the case of p−=1{p}_{-}=1. We will also prove the boundedness of the fractional maximal function associated with the Laplace-Bessel differential operator (fractional BB-maximal function) on Lp(⋅),γ(Rk,+n){L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces.Kaya EsraDe Gruyterarticleb-maximal operatorgeneralized translation operatorsingular integralsvariable exponent lebesgue spaces42a5042b2542b35MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 306-315 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	b-maximal operator generalized translation operator singular integrals variable exponent lebesgue spaces 42a50 42b25 42b35 Mathematics QA1-939
spellingShingle	b-maximal operator generalized translation operator singular integrals variable exponent lebesgue spaces 42a50 42b25 42b35 Mathematics QA1-939 Kaya Esra A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces
description	In this paper, we consider the maximal operator related to the Laplace-Bessel differential operator (BB-maximal operator) on Lp(⋅),γ(Rk,+n){L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces. We will give a necessary condition for the boundedness of the BB-maximal operator on variable exponent Lebesgue spaces. Moreover, we will obtain that the BB-maximal operator is not bounded on Lp(⋅),γ(Rk,+n){L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces in the case of p−=1{p}_{-}=1. We will also prove the boundedness of the fractional maximal function associated with the Laplace-Bessel differential operator (fractional BB-maximal function) on Lp(⋅),γ(Rk,+n){L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces.
format	article
author	Kaya Esra
author_facet	Kaya Esra
author_sort	Kaya Esra
title	A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces
title_short	A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces
title_full	A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces
title_fullStr	A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces
title_full_unstemmed	A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces
title_sort	note on maximal operators related to laplace-bessel differential operators on variable exponent lebesgue spaces
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/4748c6e8a41244f69bf3938d7df26ba5
work_keys_str_mv	AT kayaesra anoteonmaximaloperatorsrelatedtolaplacebesseldifferentialoperatorsonvariableexponentlebesguespaces AT kayaesra noteonmaximaloperatorsrelatedtolaplacebesseldifferentialoperatorsonvariableexponentlebesguespaces
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A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces

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