On the BBM-Phenomenon in Fractional Poincare-Sobolev Inequalities with Weights

被引：4

作者：

Hurri-Syrjanen, Ritva ^{[1
]}

Martinez-Perales, Javier C. ^{[2
]}

Perez, Carlos ^{[3
,4
]}

Vahakangas, Antti V. ^{[5
]}

机构：

[1] Univ Helsinki, Dept Math & Stat, Pietari Kalmin Katu 5, FI-00014 Helsinki, Finland

[2] Calle Nueva 18, Malaga 29691, Spain

[3] Univ Basque Country, Dept Math, Ikerbasque, Basque Fdn Sci, Bilbao 48009, Spain

[4] BCAM Basque Ctr Appl Math, Bilbao 48009, Spain

[5] Univ Jyvaskyla, Dept Math & Stat, POB 35, FI-40014 Jyvaskyla, Finland

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2023年 / 2023卷 / 20期

关键词：

LIMITING EMBEDDINGS; JOHN-NIRENBERG; SPACES; BOURGAIN; THEOREM; BREZIS;

D O I：

10.1093/imrn/rnac246

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we unify and improve some of the results of Bourgain, Brezis, and Mironescu and the weighted Poincare-Sobolev estimate by Fabes, Kenig, and Serapioni. More precisely, we get weighted counterparts of the Poincare-Sobolev-type inequality and also of the Hardy type inequality in the fractional case under some mild natural restrictions. A main feature of the results we obtain is the fact that we keep track of the behavior of the constants involved when the fractional parameter approaches to 1. Our main method is based on techniques coming from harmonic analysis related to the self-improving property of generalized Poincare inequalities.

引用

页码：17205 / 17244

页数：40

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