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SHARP CONSTANTS BETWEEN EQUIVALENT NORMS IN WEIGHTED LORENTZ SPACES

Part of: Linear function spaces and their duals

Published online by Cambridge University Press:  22 January 2010

SORINA BARZA  and
JAVIER SORIA
SORINA BARZA
Affiliation:
Department of Mathematics, Karlstad University, SE-65188 Karlstad, Sweden (email: sorina.barza@kau.se)
JAVIER SORIA*
Affiliation:
Department of Applied Mathematics and Analysis, University of Barcelona, E-08007 Barcelona, Spain (email: soria@ub.edu)
*
✉For correspondence; e-mail: soria@ub.edu
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Abstract

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For an increasing weight w in Bp (or equivalently in Ap), we find the best constants for the inequalities relating the standard norm in the weighted Lorentz space Λp(w) and the dual norm.

Keywords

equivalent normslevel functionweighted Lorentz spacessharp constantsweights

MSC classification

Secondary: 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 88 , Issue 1 , February 2010 , pp. 19 - 27
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

This research was partially supported by grants MTM2007-60500 and 2005SGR00556.

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