The vector valued quartile operator

  1. Tuomas P. Hytönen
  2. Michael T. Lacey
  3. Ioannis Parissis
Aldizkaria:
Collectanea mathematica

ISSN: 0010-0757

Argitalpen urtea: 2013

Alea: 64

Faszikulua: 3

Orrialdeak: 427-454

Mota: Artikulua

DOI: 10.1007/S13348-012-0070-3 DIALNET GOOGLE SCHOLAR lock_openSarbide irekia editor

Beste argitalpen batzuk: Collectanea mathematica

Garapen Iraunkorreko Helburuak

Laburpena

Certain vector-valued inequalities are shown to hold for a Walsh analog of the bilinear Hilbert transform. These extensions are phrased in terms of a recent notion of quartile type of a unconditional martingale differences (UMD) Banach space � . Every known UMD Banach space has finite quartile type, and it was recently shown that the Walsh analog of Carleson’s Theorem holds under a closely related assumption of finite tile type. For a Walsh model of the bilinear Hilbert transform however, the quartile type should be sufficiently close to that of a Hilbert space for our results to hold. A full set of inequalities is quantified in terms of quartile type.

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T.P. Hytönen and I. Parissis are supported by the European Union through the ERC Starting Grant “Analytic-probabilistic methods for borderline singular integrals”. T.P. Hytönen is also supported by the Academy of Finland, grants 130166 and 133264. M.T. Lacey supported in part by the NSF grant 0968499, and a grant from the Simons Foundation (#229596 to Michael Lacey).

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