Discrete decompositions for bilinear operators and almost diagonal conditions
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- by Loukas Grafakos and Rodolfo H. Torres
- Trans. Amer. Math. Soc. 354 (2002), 1153-1176
- DOI: https://doi.org/10.1090/S0002-9947-01-02912-9
- Published electronically: October 24, 2001
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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.References
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Bibliographic Information
- Loukas Grafakos
- Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
- MR Author ID: 288678
- ORCID: 0000-0001-7094-9201
- Email: loukas@math.missouri.edu
- Rodolfo H. Torres
- Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66049
- MR Author ID: 173635
- ORCID: 0000-0002-3777-8671
- Email: torres@math.ukans.edu
- 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 - © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 1153-1176
- MSC (1991): Primary 42B25, 42B20, 47G30; Secondary 42C15, 46E35, 35S99
- DOI: https://doi.org/10.1090/S0002-9947-01-02912-9
- MathSciNet review: 1867376