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On the notions of absolute continuity for functions of several variables

100%

Hencl S.

Fundamenta Mathematicae

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2002

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tom 173

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nr 2

175-189

EN

Absolutely continuous functions of n variables were recently introduced by J. Malý [5]. We introduce a more general definition, suggested by L. Zajíček. This new absolute continuity also implies continuity, weak differentiability with gradient in Lⁿ, differentiability almost everywhere and the area formula. It is shown that our definition does not depend on the shape of balls in the definition.

2

Absolutely continuous functions of several variables and diffeomorphisms

63%

Hencl S., Malý J.

Open Mathematics

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2003

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tom 1

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nr 4

690-705

EN

In [4], a class of absolutely continuous functions of d-variables, motivated by applications to change of variables in an integral, has been introduced. The main result of this paper states that absolutely continuous functions in the sense of [4] are not stable under diffeomorphisms. We also show an example of a function which is absolutely continuous with respect cubes but not with respect to balls.

3

Composition operator and Sobolev-Lorentz spaces $WL^{n,q}$

51%

Hencl S., Kleprlík L., Malý J.

Studia Mathematica

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2014

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tom 221

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nr 3

197-208

EN

Let Ω,Ω' ⊂ ℝⁿ be domains and let f: Ω → Ω' be a homeomorphism. We show that if the composition operator $T_{f}: u ↦ u∘ f$ maps the Sobolev-Lorentz space $WL^{n,q}(Ω')$ to $WL^{n,q}(Ω)$ for some q ≠ n then f must be a locally bilipschitz mapping.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Open Mathematics

1 Studia Mathematica

3 Hencl S.

2 Malý J.

1 Kleprlík L.

1 2014

1 2003

1 2002

On the notions of absolute continuity for functions of several variables

Absolutely continuous functions of several variables and diffeomorphisms

Composition operator and Sobolev-Lorentz spaces $WL^{n,q}$