Displaying similar documents to “An approximation theorem in higher order Orlicz-Sobolev spaces and applications”

On the continuity of Bessel potentials in Orlicz spaces.

N. Aïssaoui (1996)

Collectanea Mathematica

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It is shown that Bessel capacities in reflexive Orlicz spaces are non increasing under orthogonal projection of sets. This is used to get a continuity of potentials on some subspaces. The obtained results generalize those of Meyers and Reshetnyak in the case of Lebesgue classes.

Riesz potentials and Sobolev-type inequalities in Orlicz-Morrey spaces of an integral form

Takao Ohno, Tetsu Shimomura (2023)

Czechoslovak Mathematical Journal

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Our aim is to give Sobolev-type inequalities for Riesz potentials of functions in Orlicz-Morrey spaces of an integral form over non-doubling metric measure spaces as an extension of T. Ohno, T. Shimomura (2022). Our results are new even for the doubling metric measure spaces.

Bessel potentials in Orlicz spaces.

N. Aïssaoui (1997)

Revista Matemática de la Universidad Complutense de Madrid

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It is shown that Bessel potentials have a representation in term of measure when the underlying space is Orlicz. A comparison between capacities and Lebesgue measure is given and geometric properties of Bessel capacities in this space are studied. Moreover it is shown that if the capacity of a set is null, then the variation of all signed measures of this set is null when these measures are in the dual of an Orlicz-Sobolev space.

Fine behavior of functions whose gradients are in an Orlicz space

Jan Malý, David Swanson, William P. Ziemer (2009)

Studia Mathematica

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For functions whose derivatives belong to an Orlicz space, we develop their "fine" properties as a generalization of the treatment found in [MZ] for Sobolev functions. Of particular importance is Theorem 8.8, which is used in the development in [MSZ] of the coarea formula for such functions.