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arXiv · 1203.5604

The Vector Valued Quartile Operator

Tuomas P. Hytönen·Michael T. Lacey·Ioannis Parissis
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Abstract

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 UMD (Unconditional Martingale Differences) Banach space X. 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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Tuomas P. Hytönen, Michael T. Lacey, Ioannis Parissis. 2012-09-05. The Vector Valued Quartile Operator. https://doi.org/10.1007/s13348-012-0070-3

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