Remarks on the Bourgain-Brezis-Mironescu approach to Sobolev spaces

• Autorzy: Bojarski B.
• Języki publikacji: EN

Abstrakty

EN

For a function ƒ ∈ L[wzór] (Rⁿ) the notion of p-mean variation of order 1, V[wzór](ƒ, 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 V[wzór](ƒ, 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.

Słowa kluczowe

EN

Sobolev spaces; variation

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2011
• Tom: Vol. 59, no 1
• Strony: 65--75
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Bojarski B.

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

Bibliografia

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