Weighted estimates for dyadic paraproducts and -Haar multipliers with complexity
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...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:107332 |
| Acceso en línea: | https://ddd.uab.cat/record/107332 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_57213_01 |
| Access Level: | acceso abierto |
| Palabra clave: | Operator-weighted inequalities Dyadic paraproduct Ap-weights Haar multipliers |
| Sumario: | 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. |
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