Bilinear operators on Herz-type Hardy spaces

Authors:
Loukas Grafakos, Xinwei Li and Dachun Yang

Journal:
Trans. Amer. Math. Soc. **350** (1998), 1249-1275

MSC (1991):
Primary 47H19, 42B20, 42B30

DOI:
https://doi.org/10.1090/S0002-9947-98-01878-9

MathSciNet review:
1407489

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Abstract | References | Similar Articles | Additional Information

Abstract: The authors prove that bilinear operators given by finite sums of products of Calderón-Zygmund operators on are bounded from into if and only if they have vanishing moments up to a certain order dictated by the target space. Here are homogeneous Herz-type Hardy spaces with and . As an application they obtain that the commutator of a Calderón-Zygmund operator with a BMO function maps a Herz space into itself.

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Additional Information

**Loukas Grafakos**

Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211-0001

Email:
loukas@math.missouri.edu

**Xinwei Li**

Affiliation:
Department of Mathematics, Washington University, Campus Box 1146, St. Louis, Missouri 63130-4899

Email:
li@math.wustl.edu

**Dachun Yang**

Affiliation:
Department of Mathematics, Beijing Normal University, 100875 Beijing, The People’s Republic of China

Email:
dcyang@bnu.edu.cn

DOI:
https://doi.org/10.1090/S0002-9947-98-01878-9

Keywords:
Herz spaces,
Beurling algebras,
Hardy spaces,
atoms,
bilinear operators,
Calder\'{o}n-Zygmund operators

Received by editor(s):
January 15, 1996

Received by editor(s) in revised form:
July 15, 1996

Additional Notes:
The first author’s research was supported by the University of Missouri Research Board

Article copyright:
© Copyright 1998
American Mathematical Society