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

 

Discrete decompositions for bilinear operators and almost diagonal conditions


Authors: Loukas Grafakos and Rodolfo H. Torres
Journal: Trans. Amer. Math. Soc. 354 (2002), 1153-1176
MSC (1991): Primary 42B25, 42B20, 47G30; Secondary 42C15, 46E35, 35S99
Published electronically: October 24, 2001
MathSciNet review: 1867376
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Abstract: Using discrete decomposition techniques, bilinear operators are naturally associated with trilinear tensors. An intrinsic size condition on the entries of such tensors is introduced and is used to prove boundedness for the corresponding bilinear operators on several products of function spaces. This condition should be considered as the direct analogue of an almost diagonal condition for linear operators of Calderón-Zygmund type. Applications include a reduced $T1$ theorem for bilinear pseudodifferential operators and the extension of an $L^p$ multiplier result of Coifman and Meyer to the full range of $H^p$ spaces. The results of this article rely on decomposition techniques developed by Frazier and Jawerth and on the vector valued maximal function estimate of Fefferman and Stein.


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Additional Information

Loukas Grafakos
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: loukas@math.missouri.edu

Rodolfo H. Torres
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66049
Email: torres@math.ukans.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02912-9
PII: S 0002-9947(01)02912-9
Keywords: Singular integrals, maximal functions, Littlewood-Paley theory, almost diagonal condition, multilinear operators, wavelets, Triebel-Lizorkin spaces
Received by editor(s): May 20, 1999
Published electronically: October 24, 2001
Additional Notes: Grafakos’ research partially supported by the NSF under grant DMS 9623120
Torres’ research partially supported by the NSF under grant DMS 9696267
Article copyright: © Copyright 2001 American Mathematical Society