Hardy spaces and a Walsh model for bilinear cone operators

Gilbert, John; Nahmod, Andrea

doi:10.1090/S0002-9947-99-02490-3

Hardy spaces and a Walsh model for bilinear cone operators
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by John E. Gilbert and Andrea R. Nahmod PDF

Trans. Amer. Math. Soc. 351 (1999), 3267-3300 Request permission

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 $L^{p}$-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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