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Approximate identities and Young type inequalities in Musielak-Orlicz spaces

Fumi-Yuki Maeda, Yoshihiro Mizuta, Takao Ohno, Tetsu Shimomura (2013)

Czechoslovak Mathematical Journal

We discuss the convergence of approximate identities in Musielak-Orlicz spaces extending the results given by Cruz-Uribe and Fiorenza (2007) and the authors F.-Y. Maeda, Y. Mizuta and T. Ohno (2010). As in these papers, we treat the case where the approximate identity is of potential type and the case where the approximate identity is defined by a function of compact support. We also give a Young type inequality for convolution with respect to the norm in Musielak-Orlicz spaces.

Approximate identities in Banach function algebras

H. G. Dales, A. Ülger (2015)

Studia Mathematica

In this paper, we shall study contractive and pointwise contractive Banach function algebras, in which each maximal modular ideal has a contractive or pointwise contractive approximate identity, respectively, and we shall seek to characterize these algebras. We shall give many examples, including uniform algebras, that distinguish between contractive and pointwise contractive Banach function algebras. We shall describe a contractive Banach function algebra which is not equivalent to a uniform algebra....

Approximation and entropy numbers of compact Sobolev embeddings

Leszek Skrzypczak (2006)

Banach Center Publications

The aim of the paper is twofold. First we give a survey of some recent results concerning the asymptotic behavior of the entropy and approximation numbers of compact Sobolev embeddings. Second we prove new estimates of approximation numbers of embeddings of weighted Besov spaces in the so called limiting case.

Approximation and entropy numbers of embeddings in weighted Orlicz spaces

David Eric Edmunds, Jiong Sun (1991)

Mathematica Bohemica

Upper estimates are obtained for approximation and entropy numbers of the embeddings of weighted Sobolev spaces into appropriate weighted Orlicz spaces. Results are given when the underlying space domain is bounded and for certain unbounded domains.

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