A sharp Trudinger type inequality for harmonic functions and its applications

The present paper introduces a sharp Trudinger type inequality for harmonic functions based on the Cauchy-Riesz kernel function, which includes modified Poisson type kernel in a half plane considered by Xu et al. (Bound. Value Probl. 2013:262, 2013). As applications, we not only obtain Morrey repres...

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Detalles Bibliográficos
Autores principales: Tan, Yili, An, Yongli, Wang, Hong, Liu, Jing
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5630660/
https://www.ncbi.nlm.nih.gov/pubmed/29070933
http://dx.doi.org/10.1186/s13660-017-1522-9
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author Tan, Yili
An, Yongli
Wang, Hong
Liu, Jing
author_facet Tan, Yili
An, Yongli
Wang, Hong
Liu, Jing
author_sort Tan, Yili
collection PubMed
description The present paper introduces a sharp Trudinger type inequality for harmonic functions based on the Cauchy-Riesz kernel function, which includes modified Poisson type kernel in a half plane considered by Xu et al. (Bound. Value Probl. 2013:262, 2013). As applications, we not only obtain Morrey representations of continuous linear maps for harmonic functions in the set of all closed bounded convex nonempty subsets of any Banach space, but also deduce the representation for set-valued maps and for scalar-valued maps of Dunford-Schwartz.
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spelling pubmed-56306602017-10-23 A sharp Trudinger type inequality for harmonic functions and its applications Tan, Yili An, Yongli Wang, Hong Liu, Jing J Inequal Appl Research The present paper introduces a sharp Trudinger type inequality for harmonic functions based on the Cauchy-Riesz kernel function, which includes modified Poisson type kernel in a half plane considered by Xu et al. (Bound. Value Probl. 2013:262, 2013). As applications, we not only obtain Morrey representations of continuous linear maps for harmonic functions in the set of all closed bounded convex nonempty subsets of any Banach space, but also deduce the representation for set-valued maps and for scalar-valued maps of Dunford-Schwartz. Springer International Publishing 2017-10-06 2017 /pmc/articles/PMC5630660/ /pubmed/29070933 http://dx.doi.org/10.1186/s13660-017-1522-9 Text en © The Author(s) 2017 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
Tan, Yili
An, Yongli
Wang, Hong
Liu, Jing
A sharp Trudinger type inequality for harmonic functions and its applications
title A sharp Trudinger type inequality for harmonic functions and its applications
title_full A sharp Trudinger type inequality for harmonic functions and its applications
title_fullStr A sharp Trudinger type inequality for harmonic functions and its applications
title_full_unstemmed A sharp Trudinger type inequality for harmonic functions and its applications
title_short A sharp Trudinger type inequality for harmonic functions and its applications
title_sort sharp trudinger type inequality for harmonic functions and its applications
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5630660/
https://www.ncbi.nlm.nih.gov/pubmed/29070933
http://dx.doi.org/10.1186/s13660-017-1522-9
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