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Some geometric aspects of Sobolev spaces

Bojarski, B. — 1990

Equadiff 7

Global geometric aspects of Riemann-Hilbert problems.

Bojarski, B.; Khimshiashvili, G. — 2001

Georgian Mathematical Journal

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

B. Bojarski — 2011

Bulletin of the Polish Academy of Sciences. Mathematics

For a function $f \in L_{l o c}^{p} (ℝ ⁿ)$ the notion of p-mean variation of order 1, $₁^{p} (f, ℝ ⁿ)$ 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 $W^{1, p} (ℝ ⁿ)$ in terms of $₁^{p} (f, ℝ ⁿ)$ is directly related to the characterisation of $W^{1, p} (ℝ ⁿ)$ by Lipschitz type pointwise inequalities of Bojarski, Hajłasz and Strzelecki and to the Bourgain-Brezis-Mironescu approach.

p-harmonic equation and quasiregular mappings

B. Bojarski; T. Iwaniec — 1987

Banach Center Publications

The Muckenhoupt class A₁(R)

B. Bojarski; C. Sbordone; I. Wik — 1992

Studia Mathematica

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

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