| Date: |
2013 |
| Abstract: |
We extend the definitions of dyadic paraproduct and t-Haar multipliers to dyadic operators that depend on the complexity (m; n), for m and n natural numbers. We use the ideas developed by Nazarov and Volberg to prove that the weighted L2(w)-norm of a paraproduct with complexity (m; n), associated to a function b ∈ BMOd, depends linearly on the Ad/2-characteristic of the weight w, linearly on the BMOd-norm of b, and polynomially on the complexity. This argument provides a new proof of the linear bound for the dyadic paraproduct due to Beznosova. We also prove that the L2-norm of a t-Haar multiplier for any t ∈ R and weight w is a multiple of the square root of the Cd/2t-characteristic of w times the square root of the Ad/2-characteristic of w2t, and is polynomial in the complexity. |
| Abstract: |
The first author was supported by fellowship CAPES/FULBRIGHT, BEX 2918-06/4. |
| Rights: |
Tots els drets reservats.  |
| Language: |
Anglès |
| Document: |
Article ; recerca ; Versió publicada |
| Subject: |
Operator-weighted inequalities ;
Dyadic paraproduct ;
Ap-weights ;
Haar multipliers |
| Published in: |
Publicacions matemàtiques, Vol. 57, Núm. 2 (2013) , p. 265-294, ISSN 2014-4350 |
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