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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2021-06-01
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Online Access: | https://doi.org/10.1515/anona-2020-0187 |
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doaj-1d19a9c2594b489f80fba63331ac556b2021-10-03T07:42:25ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2021-06-01111729510.1515/anona-2020-0187Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spacesZhang Xiao0Liu Feng1Zhang Huiyun2College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, People’s Republic of ChinaCollege of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, People’s Republic of ChinaCollege of Electronic and Information Engineering, Shandong University of Science and Technology, Qingdao, Shandong 266590, People’s Republic of ChinaThis 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.https://doi.org/10.1515/anona-2020-0187variation operatorcalderón-zygmund singular integralcommutatormorrey spacebesov spaceprimary 42b2042b25 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Zhang Xiao Liu Feng Zhang Huiyun |
spellingShingle |
Zhang Xiao Liu Feng Zhang Huiyun Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces Advances in Nonlinear Analysis variation operator calderón-zygmund singular integral commutator morrey space besov space primary 42b20 42b25 |
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 |
series |
Advances in Nonlinear Analysis |
issn |
2191-9496 2191-950X |
publishDate |
2021-06-01 |
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. |
topic |
variation operator calderón-zygmund singular integral commutator morrey space besov space primary 42b20 42b25 |
url |
https://doi.org/10.1515/anona-2020-0187 |
work_keys_str_mv |
AT zhangxiao variationinequalitiesforroughsingularintegralsandtheircommutatorsonmorreyspacesandbesovspaces AT liufeng variationinequalitiesforroughsingularintegralsandtheircommutatorsonmorreyspacesandbesovspaces AT zhanghuiyun variationinequalitiesforroughsingularintegralsandtheircommutatorsonmorreyspacesandbesovspaces |
_version_ |
1716846247108673536 |