The LP Gagliardo-Nirenberg-Zhang inequality

被引：1
|
作者：
Huang, Qingzhong [1 ,2 ]
Li, Ai-Jun [3 ]
机构：
[1] Jiaxing Univ, Coll Math Phys & Informat Engn, Jiaxing 314001, Peoples R China
[2] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada
[3] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454000, Henan, Peoples R China
来源：
ADVANCES IN APPLIED MATHEMATICS | 2020年 / 113卷
关键词：
Gagliardo-Nirenberg-Zhang inequalities; Loomis-Whitney-Ball inequality; Isotropic measure; MINKOWSKI-FIREY THEORY; AFFINE; SOBOLEV; VALUATIONS;
D O I：
10.1016/j.aam.2019.101971
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the paper, the L-P version of Gagliardo-Nirenberg-Zhang inequality for isotropic measures is established. This inequality is the analytic analogue of the L-P Loomis-Whitney inequality and implies the classical L-P Sobolev inequality (without the best constant). (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页数：21
相关论文
共 50 条
  • [41] On the Gagliardo-Nirenberg type inequality in the critical Sobolev-Morrey space
    Yoshihiro Sawano
    Hidemitsu Wadade
    Journal of Fourier Analysis and Applications, 2013, 19 : 20 - 47
  • [42] On Gagliardo–Nirenberg Type Inequalities
    V. I. Kolyada
    F. J. Pérez Lázaro
    Journal of Fourier Analysis and Applications, 2014, 20 : 577 - 607
  • [43] A SHARP GAGLIARDO-NIRENBERG INEQUALITY AND ITS APPLICATION TO FRACTIONAL PROBLEMS WITH INHOMOGENEOUS NONLINEARITY
    Bhimani, Divyang G.
    Hajaiej, Hichem
    Haque, Saikatul
    LUo, Tingjian
    EVOLUTION EQUATIONS AND CONTROL THEORY, 2023, 12 (01): : 362 - 390
  • [44] On the Brezis and Mironescu conjecture concerning a Gagliardo-Nirenberg inequality for fractional Sobolev norms
    Maz'ya, V
    Shaposhnikova, T
    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2002, 81 (09): : 877 - 884
  • [45] On some nonlinear extensions of the Gagliardo-Nirenberg inequality with applications to nonlinear eigenvalue problems
    Kalamajska, Agnieszka
    Peszek, Jan
    ASYMPTOTIC ANALYSIS, 2012, 77 (3-4) : 169 - 196
  • [46] Gagliardo–Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces
    Yoshihiro Mizuta
    Eiichi Nakai
    Yoshihiro Sawano
    Tetsu Shimomura
    Archiv der Mathematik, 2012, 98 : 253 - 263
  • [47] Upper bound of the best constant of a Trudinger-Moser inequality and its application to a Gagliardo-Nirenberg inequality
    Kozono, Hideo
    Sato, Tokushi
    Wadade, Hidemitsu
    INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2006, 55 (06) : 1951 - 1974
  • [48] Gagliardo-Nirenberg inequalities on manifolds
    Badr, Nadine
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 349 (02) : 493 - 502
  • [49] On certain generalizations of the Gagliardo-Nirenberg inequality and their applications to capacitary estimates and isoperimetric inequalities
    Kaamajska, Agnieszka
    Peszek, Jan
    JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2013, 13 (01) : 271 - 290
  • [50] Note on Affine Gagliardo–Nirenberg Inequalities
    Zhichun Zhai
    Potential Analysis, 2011, 34 : 1 - 12
12345