Displaying similar documents to “Characterization of rearrangement invariant spaces with fixed points for the Hardy-Littlewood maximal operator.”

Approximate identities and Young type inequalities in Musielak-Orlicz spaces

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

Czechoslovak Mathematical Journal

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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. ...

A note on the Cahn-Hilliard equation in H 1 ( ℝ N ) involving critical exponent

Jan W. Cholewa, Aníbal Rodríguez-Bernal (2014)

Mathematica Bohemica

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We consider the Cahn-Hilliard equation in H 1 ( ℝ N ) with two types of critically growing nonlinearities: nonlinearities satisfying a certain limit condition as | u | → ∞ and logistic type nonlinearities. In both situations we prove the H 2 ( ℝ N ) -bound on the solutions and show that the individual solutions are suitably attracted by the set of equilibria. This complements the results in the literature; see J. W. Cholewa, A. Rodriguez-Bernal (2012).