Fractional Orlicz-Sobolev embeddings

被引：37
|
作者：
Alberico, Angela [1 ]
Cianchi, Andrea [2 ]
Pick, Lubos [3 ]
Slavikova, Lenka [3 ,4 ]
机构：
[1] CNR, Ist Applicaz Calcolo M Picone, Via Pietro Castellino 111, I-80131 Naples, Italy
[2] Univ Firenze, Dipartimento Matemat & Informat U Dini, Viale Morgagni 67-A, I-50134 Florence, Italy
[3] Charles Univ Prague, Fac Math & Phys, Dept Math Anal, Sokolovska 83, Prague 18675 8, Czech Republic
[4] Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany
来源：
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2021年 / 149卷
关键词：
Fractional Orlicz-Sobolev spaces; Sobolev embeddings; Hardy inequalities; Orlicz spaces; Rearrangement-invariant spaces; GAGLIARDO-NIRENBERG INEQUALITIES; LIMITING EMBEDDINGS; INTEGRAL-OPERATORS; ORDER SOBOLEV; REGULARITY; THEOREM; SPACES; IMBEDDINGS; EXTENSION; BOUNDARY;
D O I：
10.1016/j.matpur.2020.12.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz-Sobolev spaces in R-n. An improved embedding with an Orlicz-Lorentz target space, which is optimal in the broader class of all rearrangement-invariant spaces, is also established. Both spaces of order s is an element of (0, 1), and higher-order spaces are considered. Related Hardy type inequalities are proposed as well. (C) 2020 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：216 / 253
页数：38
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