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

100%

Bojarski B.

Bulletin of the Polish Academy of Sciences. Mathematics

2011

tom 59

nr 1

65-75

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.

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p-harmonic equation and quasiregular mappings

63%

Bojarski B., Iwaniec T.

Banach Center Publications

1987

tom 19

nr 1

25-38

The Muckenhoupt class A₁(R)

51%

Bojarski B., Sbordone C., Wik I.

Studia Mathematica

1991-1992

tom 101

nr 2

155-163

It is shown that the Muckenhoupt structure constants for f and f* on the real line are the same.

Ograniczanie wyników

1 Banach Center Publications

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Studia Mathematica

3 Bojarski B.

1 Iwaniec T.

1 Sbordone C.

1 Wik I.

1 2011

1 1992

1 1987

Wyniki wyszukiwania

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

p-harmonic equation and quasiregular mappings

The Muckenhoupt class A₁(R)