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Discrete decompositions for bilinear operators and almost diagonal conditions |
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| Authors: | Loukas Grafakos Rodolfo H. Torres |
| Affiliation: | Department of Mathematics, University of Missouri, Columbia, Missouri 65211 ; Department of Mathematics, University of Kansas, Lawrence, Kansas 66049 |
| 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  theorem for bilinear pseudodifferential operators and the extension of an  multiplier result of Coifman and Meyer to the full range of  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. |
| Keywords: | Singular integrals maximal functions Littlewood-Paley theory almost diagonal condition multilinear operators wavelets Triebel-Lizorkin spaces |
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