Non-smooth atomic decompositions, traces on Lipschitz domains, and\n pointwise multipliers in function spaces

2012/01/11 by Cornelia Schneider, Schneider, Cornelia, Jan Vybíral +1
Chemistry · Mathematics · #42B35 #46E35 #47B38 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Besov space #Boundary (topology) #Bounded function #Bounded variation #Chemistry #FOS: Mathematics #Function (biology) #Function space #Functional Analysis (math.FA) #Functional analysis #Interpolation space #Lipschitz continuity #Lipschitz domain #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration #Mathematical analysis #Mathematics #Pointwise #Pure mathematics #Smoothness #TRACE (psycholinguistics) #math.FA #msc:42B35 #msc:46E35 #msc:47B38

paper · pdf · doi:10.48550/arxiv.1201.2280

published in arXiv (Cornell University) (Cornell University)

arxiv created 2012/01/11 · openalex publication_date 2012/01/11 · arxiv updated 2012/01/12 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We provide non-smooth atomic decompositions for Besov spaces Bd( rn),\ns>0, 0<p,q\≤ \∞, defined via differences. The results are used to\ncompute the trace of Besov spaces on the boundary \Γ of bounded Lipschitz\ndomains \Ω with smoothness s restricted to 0<s<1 and no further\nrestrictions on the parameters p,q. We conclude with some more applications\nin terms of pointwise multipliers.\n

Citations

• Fractal Geometry: Mathematical Foundations and Applications.

Cited by

• Homogeneity property of Besov and Triebel-Lizorkin spaces

Related

• Homogeneous Sobolev and Besov spaces on special Lipschitz domains and their traces
• Non-smooth atomic decomposition of variable 2-microlocal Besov-type and Triebel-Lizorkin-type spaces
• Besov-type spaces of variable smoothness on rough domains
• Besov-Type Spaces with Variable Smoothness and Integrability
• Besov-type spaces with variable smoothness and integrability II