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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Detalles Bibliográficos
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
Descripción
Sumario: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

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