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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Autores principales: De Nápoli, P., Drelichman, I., Salort, A.
Formato: INPR
Materias:
embedding theorems
extremals
fractional Laplacian
potential spaces
power weights
Sobolev spaces
Acceso en línea: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
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spelling todo:paper_02191997_v_n_p_DeNapoli2023-10-03T15:11:06Z Weighted inequalities for the fractional Laplacian and the existence of extremals De Nápoli, P. Drelichman, I. Salort, A. 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 INPR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
De Nápoli, P.
Drelichman, I.
Salort, A.
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
format INPR
author De Nápoli, P.
Drelichman, I.
Salort, A.
author_facet De Nápoli, P.
Drelichman, I.
Salort, A.
author_sort De Nápoli, P.
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
url http://hdl.handle.net/20.500.12110/paper_02191997_v_n_p_DeNapoli
work_keys_str_mv AT denapolip weightedinequalitiesforthefractionallaplacianandtheexistenceofextremals
AT drelichmani weightedinequalitiesforthefractionallaplacianandtheexistenceofextremals
AT salorta weightedinequalitiesforthefractionallaplacianandtheexistenceofextremals
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