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5th International ISAAC Congress
July 25-30, 2005
Department of Mathematics and Informatics, University of Catania
Catania, Sicily, Italy

Organizers
International ISAAC Board, Local organizing committee: F. Nicolosi (chairman), S. Bonafede, V. Cataldo, P. Cianci, G.R. Cirmi, S. D'Asero, G. Fiorito, L. Giusti, S. Leonardi, P.E. Ricci

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Sobolev's inequality for variable exponent Riesz potentials
by
Tetsu Shimomura
Hiroshima University
Coauthors: Yoshihiro Mizuta

In this talk we study the boundedness of maximal functions in generalized Lebesgue spaces when satisfies a log-condition at infinity that is weaker than that of Cruz-Uribe, Fiorenza and Neugebauer. Our result extends the recent work of Diening and the authors. As an application of the boundedness of maximal functions, we show Sobolev's inequality for Riesz potentials with variable exponent.

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Date received: May 29, 2005

Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # card-23.