Remarks on the Bourgain-Brezis-Mironescu Approach to Sobolev Spaces

• Autorzy: B. Bojarski
• Języki publikacji: EN

Abstrakty

EN

For a function $f ∈ L_{loc}^{p}(ℝⁿ)$ the notion of p-mean variation of order 1, $𝖵₁^{p}(f,ℝⁿ)$ is defined. It generalizes the concept of F. Riesz variation of functions on the real line ℝ¹ to ℝⁿ, n > 1. The characterisation of the Sobolev space $W^{1,p}(ℝⁿ)$ in terms of $𝖵₁^{p}(f,ℝⁿ)$ is directly related to the characterisation of $W^{1,p}(ℝⁿ)$ by Lipschitz type pointwise inequalities of Bojarski, Hajłasz and Strzelecki and to the Bourgain-Brezis-Mironescu approach.

Kategorie tematyczne

• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2011
• Tom: 59
• Numer: 1
• Strony: 65-75

Daty

wydano

2011

Twórcy

autor

B. Bojarski

• Institute of Mathematics, Polish Academy of Sciences, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba59-1-8