Weighted inequalities for the fractional Laplacian and the existence of extremals-Reference-Cited by-同舟云学术

Weighted inequalities for the fractional Laplacian and the existence of extremals

Published:2019-05 Issue:03 Volume:21 Page:1850034
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

De Nápoli Pablo¹,Drelichman Irene²,Salort Ariel¹

Affiliation:

1. IMAS (UBA-CONICET) and Departamento de Matemática, Facultad de Ciencias Exactas y Naturales – Universidad de Buenos Aires, Ciudad Universitaria – 1428 Buenos Aires, Argentina

2. IMAS (UBA-CONICET), Facultad de Ciencias Exactas y Naturales – Universidad de Buenos Aires, Ciudad Universitaria – 1428 Buenos Aires, Argentina

Abstract

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].

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199718500347

Reference21 articles.

1. A Relation Between Pointwise Convergence of Functions and Convergence of Functionals

2. Stein–Weiss and Caffarelli–Kohn–Nirenberg inequalities with angular integrability

3. A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality

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