Capacities and embeddings via symmetrization and conductor inequalities

Silvestre, Pilar

doi:10.1090/S0002-9939-2013-11778-8

Capacities and embeddings via symmetrization and conductor inequalities
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Proc. Amer. Math. Soc. 142 (2014), 497-505 Request permission

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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