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Multilinear Calderón–Zygmund operators on weighted Hardy spaces

Volume 199 / 2010

Wenjuan Li, Qingying Xue, Kôzô Yabuta Studia Mathematica 199 (2010), 1-16 MSC: Primary 42B20; Secondary 42B25. DOI: 10.4064/sm199-1-1

Abstract

Grafakos–Kalton [Collect. Math. 52 (2001)] discussed the boundedness of multilinear Calderón–Zygmund operators on the product of Hardy spaces. Then Lerner et al. [Adv. Math. 220 (2009)] defined $A_{\vec{p}}$ weights and built a theory of weights adapted to multilinear Calderón–Zygmund operators. In this paper, we combine the above results and obtain some estimates for multilinear Calderón–Zygmund operators on weighted Hardy spaces and also obtain a weighted multilinear version of an inequality for multilinear fractional integrals, which is related to the classical Trudinger inequality.

Authors

  • Wenjuan LiSchool of Mathematical Sciences
    Beijing Normal University
    Laboratory of Mathematics and Complex Systems
    Ministry of Education
    Beijing 100875, P.R. China
    e-mail
  • Qingying XueSchool of Mathematical Sciences
    Beijing Normal University
    Laboratory of Mathematics and Complex Systems
    Ministry of Education
    Beijing 100875, P.R. China
    and
    Institute of Applied Physics and Computational Mathematics
    PO Box 8009, Beijing 100088, P.R. China
    and
    Department of Mathematics
    University of California
    Berkeley, CA 94720-3840, U.S.A.
    e-mail
  • Kôzô YabutaResearch Center for Mathematical Sciences
    Kwansei Gakuin University
    Gakuen 2-1, Sanda 669-1337, Japan
    e-mail

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