Weighted inequalities for the fractional Laplacian and the existence of extremals

In this paper, we obtain improved versions of Stein–Weiss and Caffarelli–Kohn–Nirenberg inequalities, involving Besov norms of negative smoothness. As an application of the former, we derive the existence of extremals of the Stein–Weiss inequality in certain cases, some of which are not contained in...

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Publicado:	2018
Materias:	embedding theorems extremals fractional Laplacian potential spaces power weights Sobolev spaces
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v_n_p_DeNapoli http://hdl.handle.net/20.500.12110/paper_02191997_v_n_p_DeNapoli
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_02191997_v_n_p_DeNapoli
record_format	dspace
spelling	paper:paper_02191997_v_n_p_DeNapoli2023-06-08T15:21:36Z Weighted inequalities for the fractional Laplacian and the existence of extremals embedding theorems extremals fractional Laplacian potential spaces power weights Sobolev spaces In this paper, we obtain improved versions of Stein–Weiss and Caffarelli–Kohn–Nirenberg inequalities, involving Besov norms of negative smoothness. As an application of the former, we derive the existence of extremals of the Stein–Weiss inequality in certain cases, some of which are not contained in the celebrated theorem of Lieb [Sharp constants in the Hardy–Littlewood–Sobolev and related inequalities, Ann. of Math. (2) 118(2) (1983) 101–116]. © 2018 World Scientific Publishing Company 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v_n_p_DeNapoli http://hdl.handle.net/20.500.12110/paper_02191997_v_n_p_DeNapoli
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	embedding theorems extremals fractional Laplacian potential spaces power weights Sobolev spaces
spellingShingle	embedding theorems extremals fractional Laplacian potential spaces power weights Sobolev spaces Weighted inequalities for the fractional Laplacian and the existence of extremals
topic_facet	embedding theorems extremals fractional Laplacian potential spaces power weights Sobolev spaces
description	In this paper, we obtain improved versions of Stein–Weiss and Caffarelli–Kohn–Nirenberg inequalities, involving Besov norms of negative smoothness. As an application of the former, we derive the existence of extremals of the Stein–Weiss inequality in certain cases, some of which are not contained in the celebrated theorem of Lieb [Sharp constants in the Hardy–Littlewood–Sobolev and related inequalities, Ann. of Math. (2) 118(2) (1983) 101–116]. © 2018 World Scientific Publishing Company
title	Weighted inequalities for the fractional Laplacian and the existence of extremals
title_short	Weighted inequalities for the fractional Laplacian and the existence of extremals
title_full	Weighted inequalities for the fractional Laplacian and the existence of extremals
title_fullStr	Weighted inequalities for the fractional Laplacian and the existence of extremals
title_full_unstemmed	Weighted inequalities for the fractional Laplacian and the existence of extremals
title_sort	weighted inequalities for the fractional laplacian and the existence of extremals
publishDate	2018
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v_n_p_DeNapoli http://hdl.handle.net/20.500.12110/paper_02191997_v_n_p_DeNapoli
_version_	1768546673479385088

Weighted inequalities for the fractional Laplacian and the existence of extremals

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