Capacities and embeddings via symmetrization and conductor inequalities
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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.References
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Additional Information
- Pilar Silvestre
- Affiliation: Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Barcelona, Spain
- Email: pilar.silvestre@gmail.com
- 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
- © Copyright 2013 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 497-505
- MSC (2000): Primary 46E30; Secondary 28A12
- DOI: https://doi.org/10.1090/S0002-9939-2013-11778-8
- MathSciNet review: 3133991