An L¹-type estimate for Riesz potentials

Schikorra, Armin;Spector, Daniel;Van Schaftingen, Jean
(2017) Revista Matematica Iberoamericana — Vol. 33, n° 1, p. 291-303 (2017)

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Authors
  • Schikorra, ArminAlbert-Ludwigs-Universität Freiburg
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  • Spector, DanielNational Chiao Tung University
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  • Van Schaftingen, Jeanorcid-logoUCLouvain
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Abstract
In this paper we establish new L1-type estimates for the classical Riesz potentials of order α∈(0,N): ∥Iαu∥LN/(N−α)(RN)≤C∥Ru∥L1(RN;RN). This sharpens the result of Stein and Weiss on the mapping properties of Riesz potentials on the real Hardy space H¹(RN) and provides a new family of L¹-Sobolev inequalities for the Riesz fractional gradient.
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Schikorra, A., Spector, D., & Van Schaftingen, J. (2017). An L¹-type estimate for Riesz potentials. Revista Matematica Iberoamericana, 33(1), 291-303. https://doi.org/10.4171/rmi/937 (Original work published 2017)