Integrable cross sections in mixed-norm spaces and Sobolev embeddings

被引：0
作者：
Nadia Clavero
Javier Soria
机构：
[1] University of Barcelona,Department of Applied Mathematics and Analysis
来源：
Positivity | 2016年 / 20卷
关键词：
Rearrangement-invariant spaces; Mixed-norm spaces; Embeddings; Lorentz spaces; 46E35; 46E30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We characterize optimal Sobolev embeddings in terms of integrable cross sections and mixed-norm spaces, involving general rearrangement-invariant estimates. We also find the optimal domains and ranges for these embeddings.
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页码：435 / 466
页数：31
相关论文
共 30 条
  • [1] Algervik R(2011)On Fournier–Gagliardo mixed norm spaces Ann. Acad. Sci. Fenn. Math. 36 493-508
  • [2] Kolyada VI(2006)Mixed norm and multidimensional Lorentz spaces Positivity 10 539-554
  • [3] Barza S(1961)The space Duke Math. J. 28 301-324
  • [4] Kamińska A(1981), with mixed norm Trans. Am. Math. Soc. 263 149-167
  • [5] Persson L(2002)Multivariate rearrangements and Banach function spaces with mixed norms Positivity 6 393-411
  • [6] Soria J(2008)Some inequalities in classical spaces with mixed norms J. Anal. Math. 105 241-265
  • [7] Benedek A(2014)Boundary trace inequalities and rearrangements J. Math. Anal. Appl. 419 878-903
  • [8] Panzone R(2000)Mixed norm spaces and rearrangement invariant estimates J. Funct. Anal. 170 307-355
  • [9] Blozinski AP(1958)Optimal Sobolev imbeddings involving rearrangement-invariant quasinorms Ricerche Mat. 7 102-137
  • [10] Boccuto A(1970)Proprietà di alcune classi di funzioni in più variabili Math. Scand. 26 177-199
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