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

15 pages
Read Article

Loading next page...
 
/lp/springer_journal/non-homogeneous-tb-theorem-for-bi-parameter-g-function-daiWhvcLcu
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
D.O.I.
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.

You’re reading a free preview. Subscribe to read the entire article.

Try 2 weeks free now

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

or browse the journals available

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off

Sign up
for free
Start 14 day
Free Trial