Title: An L-1-type estimate for Riesz potentials
Authors: Schikorra, Armin
Spector, Daniel
Van Schaftingen, Jean
Department of Applied Mathematics
Keywords: Riesz potentials;Riesz transforms;Sobolev inequalities;fractional gradient
Issue Date: 1-Jan-2017
Abstract: In this paper we establish new L-1-type estimates for the classical Riesz potentials of order alpha is an element of (0, N): parallel to I alpha u parallel to N-L/(N-alpha)(R-N) <= C parallel to Ru parallel to (L1(RN; RN)). This sharpens the result of Stein and Weiss on the mapping properties of Riesz potentials on the real Hardy space H-1 (R-N) and provides a new family of L-1-Sobolev inequalities for the Riesz fractional gradient.
URI: http://dx.doi.org/10.4171/RMI/937
ISSN: 0213-2230
DOI: 10.4171/RMI/937
Volume: 33
Begin Page: 291
End Page: 303
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