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Pàgina inicial > Articles > Articles publicats > On restricted weak-type constants of Fourier multipliers |
Data: | 2014 |
Resum: | 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. |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió publicada |
Matèria: | Fourier multiplier ; Singular integral ; Beurling-Ahlfors transform ; Martingale ; Differential subordination |
Publicat a: | Publicacions matemàtiques, Vol. 58, Núm. 2 (2014) , p. 415-443, ISSN 2014-4350 |
29 p, 474.6 KB |