2012/11/06 by V. I. Kolyada, Kolyada, V. I., J. Pérez Lázaro +2 · 1 citation
Mathematics · #26D10 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Primary 46E35 #Secondary 46E30 #math.CA #math.FA #msc:26D10 #msc:46E30 #msc:46E35
paper · pdf · doi:10.48550/arxiv.1211.1315
arxiv created 2012/11/06 · openalex publication_date 2012/11/06 · arxiv updated 2012/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a Gagliardo-Nirenberg inequality which bounds Lorentz norms of the function by Sobolev norms and homogeneous Besov quasinorms with negative smoothness. We prove also other versions involving Besov or Triebel-Lizorkin quasinorms. These inequalities can be considered as refinements of Sobolev type embeddings. They can also be applied to obtain Gagliardo-Nirenberg inequalities in some limiting cases. Our methods are based on estimates of rearrangements in terms of heat kernels. These methods enable us to cover also the case of Sobolev norms with p = 1.