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On restricted weak-type constants of Fourier multipliers
Osekowski, Adam (University of Warsaw. Department of Mathematics, Informatics and Mechanics)

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 ; publishedVersion
Matèria: Fourier multiplier ; Singular integral ; Beurling-Ahlfors transform ; Martingale ; Differential subordination
Publicat a: Publicacions matemàtiques, Vol. 58, Núm. 2 (2014) , p. 415-443, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_58214_21

29 p, 474.6 KB

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