Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces

This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels...

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Autores principales:	Zhang Xiao, Liu Feng, Zhang Huiyun
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	variation operator calderón-zygmund singular integral commutator morrey space besov space primary 42b20 42b25 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/1d19a9c2594b489f80fba63331ac556b
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id	oai:doaj.org-article:1d19a9c2594b489f80fba63331ac556b
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spelling	oai:doaj.org-article:1d19a9c2594b489f80fba63331ac556b2021-12-05T14:10:40ZVariation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces2191-94962191-950X10.1515/anona-2020-0187https://doaj.org/article/1d19a9c2594b489f80fba63331ac556b2021-06-01T00:00:00Zhttps://doi.org/10.1515/anona-2020-0187https://doaj.org/toc/2191-9496https://doaj.org/toc/2191-950XThis paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq(Sn−1) (q > 1) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces. In addition, we present a criterion on the boundedness and continuity for a class of variation operators of singular integrals and their commutators on Besov spaces. As applications, we obtain the boundedness and continuity for the variation operators of Hilbert transform, Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators on Besov spaces.Zhang XiaoLiu FengZhang HuiyunDe Gruyterarticlevariation operatorcalderón-zygmund singular integralcommutatormorrey spacebesov spaceprimary 42b2042b25AnalysisQA299.6-433ENAdvances in Nonlinear Analysis, Vol 11, Iss 1, Pp 72-95 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	variation operator calderón-zygmund singular integral commutator morrey space besov space primary 42b20 42b25 Analysis QA299.6-433
spellingShingle	variation operator calderón-zygmund singular integral commutator morrey space besov space primary 42b20 42b25 Analysis QA299.6-433 Zhang Xiao Liu Feng Zhang Huiyun Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces
description	This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq(Sn−1) (q > 1) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces. In addition, we present a criterion on the boundedness and continuity for a class of variation operators of singular integrals and their commutators on Besov spaces. As applications, we obtain the boundedness and continuity for the variation operators of Hilbert transform, Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators on Besov spaces.
format	article
author	Zhang Xiao Liu Feng Zhang Huiyun
author_facet	Zhang Xiao Liu Feng Zhang Huiyun
author_sort	Zhang Xiao
title	Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces
title_short	Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces
title_full	Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces
title_fullStr	Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces
title_full_unstemmed	Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces
title_sort	variation inequalities for rough singular integrals and their commutators on morrey spaces and besov spaces
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/1d19a9c2594b489f80fba63331ac556b
work_keys_str_mv	AT zhangxiao variationinequalitiesforroughsingularintegralsandtheircommutatorsonmorreyspacesandbesovspaces AT liufeng variationinequalitiesforroughsingularintegralsandtheircommutatorsonmorreyspacesandbesovspaces AT zhanghuiyun variationinequalitiesforroughsingularintegralsandtheircommutatorsonmorreyspacesandbesovspaces
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Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces

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