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Hardy Spaces and a Walsh Model for Bilinear Cone Operators

John E. Gilbert and Andrea R. Nahmod
Transactions of the American Mathematical Society
Vol. 351, No. 8 (Aug., 1999), pp. 3267-3300
Stable URL: http://www.jstor.org/stable/118021
Page Count: 34
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Hardy Spaces and a Walsh Model for Bilinear Cone Operators
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Abstract

The study of bilinear operators associated to a class of non-smooth symbols can be reduced to ther study of certain special bilinear cone operators to which a time frequency analysis using smooth wave-packets is performed. In this paper we prove that when smooth wave-packets are replaced by Walsh wave-packets the corresponding discrete Walsh model for the cone operators is not only Lp-bounded as Thiele has shown in his thesis for the Walsh model corresponding to the bilinear Hilbert transform, but actually improves regularity as it maps into a Hardy space. The same result is expected to hold for the special bilinear cone operators.

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