An approximation theorem in higher order Orlicz-Sobolev spaces and applications
A. Benkirane, J.-P. Gossez (1989)
Studia Mathematica
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Displaying similar documents to “Lorentz-Karamata spaces, Bessel and Riesz potentials and embeddings”
An approximation theorem in higher order Orlicz-Sobolev spaces and applications
On the continuity of strongly nonlinear potential
Noureddine Aïssaoui (2001)
Mathematica Slovaca
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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.
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.
Boundedness of convolution operators with smooth kernels on Orlicz spaces
Hugo Aimar, Eleonor Harboure, Bibiana Iaffei (2002)
Studia Mathematica
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We study boundedness in Orlicz norms of convolution operators with integrable kernels satisfying a generalized Lipschitz condition with respect to normal quasi-distances of ℝⁿ and continuity moduli given by growth functions.
Continuity properties of functions from Orlicz-Sobolev spaces and embedding theorems
Andrea Cianchi (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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On factorization of Fefferman's inequality
Krbec, Miroslav, Schott, Thomas
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Compact and continuous embeddings of logarithmic Bessel potential spaces
David E. Edmunds, Petr Gurka, Bohumír Opic (2005)
Studia Mathematica
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We establish compact and continuous embeddings for Bessel potential spaces modelled upon generalized Lorentz-Zygmund spaces. The target spaces are either of Lorentz-Zygmund or Hölder type.
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.
Musielak-Orlicz-Sobolev spaces on metric measure spaces
Takao Ohno, Tetsu Shimomura (2015)
Czechoslovak Mathematical Journal
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Our aim in this paper is to study Musielak-Orlicz-Sobolev spaces on metric measure spaces. We consider a Hajłasz-type condition and a Newtonian condition. We prove that Lipschitz continuous functions are dense, as well as other basic properties. We study the relationship between these spaces, and discuss the Lebesgue point theorem in these spaces. We also deal with the boundedness of the Hardy-Littlewood maximal operator on Musielak-Orlicz spaces. As an application of the boundedness...