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Triebel-Lizorkin space boundedness of rough singular integrals associated to surfaces of revolution

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Abstract

We consider the boundedness of the rough singular integral operator T Ω,ψ,h along a surface of revolution on the Triebel-Lizorkin space \(\dot F_{p,q}^\alpha (\mathbb{R}^n )\) for Ω ∈ H 1(S n−1) and Ω ∈ L log+L(S n−1) ∪ (U1<q<∞ B (0,0) q (S n−1)), respectively.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, China

    Yong Ding

  2. Research Center for Mathematical Sciences, Kwansei Gakuin University, Gakuen 2-1, Sanda, 669-1337, Japan

    Kôzô Yabuta

Authors
  1. Yong Ding
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  2. Kôzô Yabuta
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Correspondence to Yong Ding.

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Ding, Y., Yabuta, K. Triebel-Lizorkin space boundedness of rough singular integrals associated to surfaces of revolution. Sci. China Math. 59, 1721–1736 (2016). https://doi.org/10.1007/s11425-016-5154-1

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  • DOI: https://doi.org/10.1007/s11425-016-5154-1

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