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

页码：216 / 253

页数：38

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