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A note on weighted bounds for singular operators with nonsmooth kernels

Tom 236 / 2017

The Anh Bui, José M. Conde-Alonso, Xuan Thinh Duong, Mahdi Hormozi Studia Mathematica 236 (2017), 245-269 MSC: Primary 42B20; Secondary 42B25. DOI: 10.4064/sm8409-9-2016 Opublikowany online: 20 January 2017

Streszczenie

Let $T$ be a multilinear {integral} operator which is bounded on certain products of Lebesgue spaces on $\mathbb R^n$. We assume that its associated kernel satisfies some mild regularity condition which is weaker than the usual Hölder continuity of kernels of multilinear Calderón–Zygmund singular integral operators. In this paper, given a suitable multiple weight $\vec{w}$, we obtain a bound for the weighted norm of $T$ in terms of $\vec{w}$. As applications, we obtain new weighted bounds for certain singular integral operators such as linear and multilinear Fourier multipliers and the Riesz transforms associated to Schrödinger operators on $\mathbb {R}^n$.

Autorzy

  • The Anh BuiDepartment of Mathematics
    Macquarie University
    North Ryde, NSW 2109, Australia
    e-mail
    e-mail
  • José M. Conde-AlonsoInstituto de Ciencias Matemáticas
    Consejo Superior de Investigaciones Científicas
    C/ Nicolás Cabrera 13-15
    28049 Madrid, Spain
    e-mail
  • Xuan Thinh DuongDepartment of Mathematics
    Macquarie University
    North Ryde, NSW 2109, Australia
    e-mail
  • Mahdi HormoziDepartment of Mathematical Sciences
    Division of Mathematics
    University of Gothenburg
    41296 Gothenburg, Sweden
    and
    Department of Mathematics
    Shiraz University
    Shiraz 71454, Iran
    e-mail

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