The vector valued quartile operator
- Tuomas P. Hytönen
- Michael T. Lacey
- Ioannis Parissis
ISSN: 0010-0757
Ano de publicación: 2013
Volume: 64
Fascículo: 3
Páxinas: 427-454
Tipo: Artigo
Outras publicacións en: Collectanea mathematica
Obxectivos de Desenvolvemento Sustentable
Resumo
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.
Información de financiamento
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).Financiadores
-
National Science Foundation
United States
- 1265570
-
Simons Foundation
United States
- 229596
-
Seventh Framework Programme
European Union
- 278558
- European Commission European Union
- European Research Council European Union
-
Academy of Finland
Finland
- 133264