Projects per year
Abstract
We complete our theory of weighted
L-p (w(1)) x L-q (w(2)) -> L-r (w(1)(r/p) w(2)(r/q))
estimates for bilinear bi-parameter Calderon-Zygmund operators under the assumption that w(1) is an element of A(p) and w(2 )is an element of A(q) are bi-parameter weights. This is done by lifting a previous restriction on the class of singular integrals by extending a classical result of Muckenhoupt and Wheeden regarding weighted BMO spaces to the product BMO setting. We use this extension of the Muckenhoupt-Wheeden result also to generalise some two-weight commutator estimates from biparameter to multi-parameter. This gives a fully satisfactory Bloom-type upper estimate for [T-1, [T-2, ...[b,T-k]]], where each T-i can be a completely general multi-parameter Calderon-Zygmund operator.
L-p (w(1)) x L-q (w(2)) -> L-r (w(1)(r/p) w(2)(r/q))
estimates for bilinear bi-parameter Calderon-Zygmund operators under the assumption that w(1) is an element of A(p) and w(2 )is an element of A(q) are bi-parameter weights. This is done by lifting a previous restriction on the class of singular integrals by extending a classical result of Muckenhoupt and Wheeden regarding weighted BMO spaces to the product BMO setting. We use this extension of the Muckenhoupt-Wheeden result also to generalise some two-weight commutator estimates from biparameter to multi-parameter. This gives a fully satisfactory Bloom-type upper estimate for [T-1, [T-2, ...[b,T-k]]], where each T-i can be a completely general multi-parameter Calderon-Zygmund operator.
Original language | English |
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Journal | Indiana University Mathematics Journal |
Volume | 71 |
Issue number | 1 |
Pages (from-to) | 37-63 |
Number of pages | 27 |
ISSN | 0022-2518 |
DOIs | |
Publication status | Published - 2022 |
MoE publication type | A1 Journal article-refereed |
Fields of Science
- 111 Mathematics
- Bilinear analysis
- bi-parameter analysis
- model operators
- weighted estimates
- SINGULAR-INTEGRALS
- EXTRAPOLATION
- REPRESENTATION
- INEQUALITIES
- OPERATORS
- BMO
Projects
- 2 Finished
-
Singular integrals and the geometry of measures
Martikainen, H. & Oikari, T.
Valtion perusrahoitus/hankkeet
01/01/2018 → 31/12/2020
Project: University of Helsinki Three-Year Research Project
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Geometric and dyadic harmonic analysis: general measures and rectifiability
Martikainen, H. & Airta, E.
01/09/2016 → 31/08/2021
Project: Research project