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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hardy spaces and a Walsh model
for bilinear cone operators


Authors: John E. Gilbert and Andrea R. Nahmod
Journal: Trans. Amer. Math. Soc. 351 (1999), 3267-3300
MSC (1991): Primary 42B15, 42B30.; Secondary 42B25
Published electronically: March 29, 1999
MathSciNet review: 1665331
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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 $L^{p}$-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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Additional Information

John E. Gilbert
Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712-1082
Email: gilbert@linux53.ma.utexas.edu

Andrea R. Nahmod
Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712-1082
Address at time of publication: Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003-4515
Email: nahmod@math.umass.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02490-3
PII: S 0002-9947(99)02490-3
Received by editor(s): April 11, 1997
Published electronically: March 29, 1999
Dedicated: In memory of J.-A. Chao
Article copyright: © Copyright 1999 American Mathematical Society