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Non-homogeneous Tb Theorem for Bi-parameter g-function

Non-homogeneous Tb Theorem for Bi-parameter g-function The main result of this paper is a bi-parameter Tb theorem for Littlewood–Paley g-function, where b is a tensor product of two pseudo-accretive function. Instead of the doubling measure, we work with a product measure μ = μ n × μ m , where the measures μ n and μ m are only assumed to be upper doubling. The main techniques of the proof include a bi-parameter b-adapted Haar function decomposition and an averaging identity over good double Whitney regions. Moreover, the non-homogeneous analysis and probabilistic methods are used again. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Sinica, English Series Springer Journals

Non-homogeneous Tb Theorem for Bi-parameter g-function

Cao, Ming; Xue, Qing
Acta Mathematica Sinica, English Series , Volume 34 (9) – May 23, 2018
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Publisher
Springer Journals
Copyright
Copyright © 2018 by Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1439-8516
eISSN
1439-7617
DOI
10.1007/s10114-018-7431-0
Publisher site
See Article on Publisher Site

Abstract

The main result of this paper is a bi-parameter Tb theorem for Littlewood–Paley g-function, where b is a tensor product of two pseudo-accretive function. Instead of the doubling measure, we work with a product measure μ = μ n × μ m , where the measures μ n and μ m are only assumed to be upper doubling. The main techniques of the proof include a bi-parameter b-adapted Haar function decomposition and an averaging identity over good double Whitney regions. Moreover, the non-homogeneous analysis and probabilistic methods are used again.

Journal

Acta Mathematica Sinica, English Series – Springer Journals

Published: May 23, 2018

References

  • A Characterization of two weight norm inequality for Littlewood–Paley g λ*-function
    Cao, M.; Li, K.; Xue, Q.
  • A non-homogeneous local Tb theorem for Littlewood–Paley g λ*-function with Lp-testing condition
    Cao, M.; Xue, Q.
  • Singular integrals on product spaces
    Fefferman, R. S. E.
  • The vector-valued non-homogeneous Tb theorem
    Hytönen, T.
  • The sharp weighted bound for general Calderón–Zygmund operators
    Hytönen, T.
  • Non-homogeneous T1 theorem for bi-parameter singular integrals
    Hytönen, T.; Martikainen, H.
  • The Hardy space H 1 on non-homogeneous metric spaces
    Hytönen, T.; Yang, D.; Yang, D.
  • Calderón–Zygmund operators on product spaces
    Journé, J. L.
  • Two weight norm inequalities for g function
    Lacey, M. T.; Li, K.
  • Representation of bi-parameter singular integrals by dyadic operators
    Martikainen, H.
  • Boundedness of a class of bi-parameter square function in the upper half-space
    Martikainen, H.
  • Square functions with general measures
    Martikainen, H. M. M.
  • Cauchy integral and Calderón–Zygmund operators on nonhomogeneous spaces
    Nazarov, F.; Treil, S.; Volberg, A.
  • The Tb-theorem on non-homogeneous spaces
    Nazarov, F.; Treil, S.; Volberg, A.
  • A T(b) theorem on product spaces
    Ou, Y.
  • Multi-parameter singular integral operators and representation theorem
    Ou, Y.
  • Higher order Journé commutators and characterizations of multiparameter BMO
    Ou, Y.; Petermichl, S.; Strousec, E.
  • A T(1) theorem on product spaces
    Pott, S.; Villarroya, P.

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