A note on Marcinkiewicz integrals supported by submanifolds

In the present paper, we establish the boundedness and continuity of the parametric Marcinkiewicz integrals with rough kernels associated to polynomial mapping [Formula: see text] as well as the corresponding compound submanifolds, which is defined by [Formula: see text] on the Triebel–Lizorkin spac...

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Detalles Bibliográficos
Autor principal: Liu, Feng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6132579/
https://www.ncbi.nlm.nih.gov/pubmed/30839656
http://dx.doi.org/10.1186/s13660-018-1822-8
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author Liu, Feng
author_facet Liu, Feng
author_sort Liu, Feng
collection PubMed
description In the present paper, we establish the boundedness and continuity of the parametric Marcinkiewicz integrals with rough kernels associated to polynomial mapping [Formula: see text] as well as the corresponding compound submanifolds, which is defined by [Formula: see text] on the Triebel–Lizorkin spaces and Besov spaces when [Formula: see text] and [Formula: see text] for some [Formula: see text] . Our main results represent significant improvements and natural extensions of what was known previously.
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spelling pubmed-61325792018-09-13 A note on Marcinkiewicz integrals supported by submanifolds Liu, Feng J Inequal Appl Research In the present paper, we establish the boundedness and continuity of the parametric Marcinkiewicz integrals with rough kernels associated to polynomial mapping [Formula: see text] as well as the corresponding compound submanifolds, which is defined by [Formula: see text] on the Triebel–Lizorkin spaces and Besov spaces when [Formula: see text] and [Formula: see text] for some [Formula: see text] . Our main results represent significant improvements and natural extensions of what was known previously. Springer International Publishing 2018-09-04 2018 /pmc/articles/PMC6132579/ /pubmed/30839656 http://dx.doi.org/10.1186/s13660-018-1822-8 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Liu, Feng
A note on Marcinkiewicz integrals supported by submanifolds
title A note on Marcinkiewicz integrals supported by submanifolds
title_full A note on Marcinkiewicz integrals supported by submanifolds
title_fullStr A note on Marcinkiewicz integrals supported by submanifolds
title_full_unstemmed A note on Marcinkiewicz integrals supported by submanifolds
title_short A note on Marcinkiewicz integrals supported by submanifolds
title_sort note on marcinkiewicz integrals supported by submanifolds
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6132579/
https://www.ncbi.nlm.nih.gov/pubmed/30839656
http://dx.doi.org/10.1186/s13660-018-1822-8
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