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Capacities and embeddings via symmetrization and conductor inequalities

Author: Pilar Silvestre
Journal: Proc. Amer. Math. Soc. 142 (2014), 497-505
MSC (2000): Primary 46E30; Secondary 28A12
Published electronically: October 11, 2013
MathSciNet review: 3133991
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Abstract: Using estimates of rearrangements in terms of modulus of continuity, some isocapacitary inequalities are derived for Besov, Lipschitz or $ H^{\omega }_p$ capacities. These inequalities allow us to show that capacitary Lorentz spaces, based on Besov spaces, are between the homogeneous Besov spaces and the usual Lorentz spaces. Moreover, we extend a result of Adams-Xiao to other function spaces and we improve embeddings of Lipschitz and $ H^{\omega }_p$ spaces in Lorentz spaces.

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Additional Information

Pilar Silvestre
Affiliation: Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Barcelona, Spain

Keywords: Rearrangement estimates, function spaces, modulus of continuity, isocapacitary inequalities, embeddings
Received by editor(s): December 8, 2011
Received by editor(s) in revised form: March 5, 2012, and March 15, 2012
Published electronically: October 11, 2013
Additional Notes: This work was partially supported by Grant MTM2010-14946 and by a grant from the Ferran Sunyer i Balaguer Foundation
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2013 American Mathematical Society

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