Bilinear operators on Herz-type Hardy spaces
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- by Loukas Grafakos, Xinwei Li and Dachun Yang PDF
- Trans. Amer. Math. Soc. 350 (1998), 1249-1275 Request permission
Abstract:
The authors prove that bilinear operators given by finite sums of products of Calderón-Zygmund operators on $\mathbb {R}^{n}$ are bounded from $H\dot K_{q_{1}}^{\alpha _{1},p_{1}}\times H\dot K_{q_{2}}^{\alpha _{2},p_{2}}$ into $H\dot K_{q}^{\alpha ,p}$ if and only if they have vanishing moments up to a certain order dictated by the target space. Here $H\dot K_{q}^{\alpha ,p}$ are homogeneous Herz-type Hardy spaces with $1/p=1/p_{1}+1/p_{2},$ $0<p_{i}\le \infty ,$ $1/q=1/q_{1}+1/q_{2},$ $1<q_{1},q_{2}<\infty ,$ $1\le q<\infty ,$ $\alpha =\alpha _{1}+\alpha _{2}$ and $-n/q_{i}<\alpha _{i}<\infty$. As an application they obtain that the commutator of a Calderón-Zygmund operator with a BMO function maps a Herz space into itself.References
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Additional Information
- Loukas Grafakos
- Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211-0001
- MR Author ID: 288678
- ORCID: 0000-0001-7094-9201
- 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
- MR Author ID: 317762
- Email: dcyang@bnu.edu.cn
- 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
- © Copyright 1998 American Mathematical Society
- 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