Interpolation inequalities between Sobolev and Morrey-Campanato spaces: A common gateway to concentration-compactness and Gagliardo-Nirenberg interpolation inequalities

被引：16

作者：

Van Schaftingen, Jean ^{[1
]}

机构：

[1] Catholic Univ Louvain, Inst Rech Math & Phys, B-1348 Louvain La Neuve, Belgium

来源：

PORTUGALIAE MATHEMATICA | 2014年 / 71卷 / 3-4期

关键词：

Sobolev space; Morrey space; Campanato space; interpolation inequality; functions of bounded mean oscillation; Holder continuous functions; Zygmund class; higherorder derivative; fractional Sobolev space; Besov space; improved Sobolev embedding; concentration-compactness; ELLIPTIC-EQUATIONS;

D O I：

10.4171/PM/1947

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove interpolation estimates between Morrey-Campanato spaces and Sobolev spaces. These estimates give in particular concentration-compactness inequalities in the translation-invariant and in the translation- and dilation-invariant case. They also give in particular interpolation estimates between Sobolev spaces and functions of bounded mean oscillation. The proofs rely on Sobolev integral representation formulae and maximal function theory. Fractional Sobolev spaces are also covered.

引用

页码：159 / 175

页数：17

共 16 条

[1] GAGLIARDO-NIRENBERG AND SOBOLEV INTERPOLATION INEQUALITIES ON BESOV SPACES
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Nguyen Lam
Lu, Guozhen
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2022, 150 (02) : 605 - 616
[2] John-Nirenberg Type Inequalities for the Morrey-Campanato Spaces
Wenming Li
[J]. Journal of Inequalities and Applications, 2008
[3] John-Nirenberg type inequalities for the Morrey-Campanato spaces
Li, Wenming
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2008, 2008 (1)
[4] Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenb erg interpolation inequalities associated with Coulomb-Sobolev spaces
Mallick, Arka
Nguyen, Hoai-Minh
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2022, 283 (10)
[5] Vector-valued Sobolev spaces and Gagliardo-Nirenberg inequalities
Schmeisser, HJ
Sickel, W
[J]. Nonlinear Elliptic and Parabolic Problems: A SPECIAL TRIBUTE TO THE WORK OF HERBERT AMANN, MICHEL CHIPOT AND JOACHIM ESCHER, 2005, 64 : 463 - 472
[6] Gagliardo-Nirenberg, Trudinger-Moser and Morrey inequalities on Dirichlet spaces
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Baudoin, Fabrice
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 497 (02)
[7] SHARP GAGLIARDO-NIRENBERG INEQUALITIES IN FRACTIONAL COULOMB-SOBOLEV SPACES
Bellazzini, Jacopo
Ghimenti, Marco
Mercuri, Carlo
Moroz, Vitaly
Van Schaftingen, Jean
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 370 (11) : 8285 - 8310
[8] Generalized Gagliardo-Nirenberg inequalities using Lorentz spaces, BMO, Holder spaces and fractional Sobolev spaces
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Diaz, Jesus Ildefonso
Quoc-Hung Nguyen
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2018, 173 : 146 - 153
[9] Sharp weighted Sobolev and Gagliardo-Nirenberg inequalities on half-spaces via mass transport and consequences
Van Hoang Nguyen
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2015, 111 : 127 - 148
[10] Quantitative Estimates of Embedding Constants for Gagliardo-Nirenberg Inequalities on Critical Sobolev-Besov-Lorentz Spaces
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[J]. Journal of Fourier Analysis and Applications, 2013, 19 : 1029 - 1059

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