On restricted weak-type constants of Fourier multipliers
We exhibit a large class of symbols m: Rd ! C for which the corresponding Fourier multipliers Tm satisfy the following restricted weak-type estimates: if A Rd has finite Lebesgue measure, then... In particular, this leads to novel sharp estimates for the real and imaginary part of the Beurling-Ahlfo...
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| Formato: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:119038 |
| Acesso em linha: | https://ddd.uab.cat/record/119038 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_58214_21 |
| Access Level: | acceso abierto |
| Palavra-chave: | Fourier multiplier Singular integral Beurling-Ahlfors transform Martingale Differential subordination |
| Resumo: | We exhibit a large class of symbols m: Rd ! C for which the corresponding Fourier multipliers Tm satisfy the following restricted weak-type estimates: if A Rd has finite Lebesgue measure, then... In particular, this leads to novel sharp estimates for the real and imaginary part of the Beurling-Ahlfors operator on C. The proof rests on probabilistic methods: we exploit a stochastic representation of the multipliers in terms of Lévy processes and appropriate sharp inequalities for differentially subordinated martingales. |
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