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An embedding theorem for Sobolev type functions with gradients in a Lorentz space

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Ranjbar-Motlagh A.

Studia Mathematica

2009

tom 191

nr 1

1-9

The purpose of this paper is to prove an embedding theorem for Sobolev type functions whose gradients are in a Lorentz space, in the framework of abstract metric-measure spaces. We then apply this theorem to prove absolute continuity and differentiability of such functions.

A note on the Poincaré inequality

100%

Ranjbar-Motlagh A.

Studia Mathematica

2003

tom 154

nr 1

1-11

The Poincaré inequality is extended to uniformly doubling metric-measure spaces which satisfy a version of the triangle comparison property. The proof is based on a generalization of the change of variables formula.

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2 Studia Mathematica

2 Ranjbar-Motlagh A.

1 2009

1 2003

Wyniki wyszukiwania

An embedding theorem for Sobolev type functions with gradients in a Lorentz space

A note on the Poincaré inequality