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Title: Multilinear operators with non-smooth kernels and commutators of singular integrals
Related: Transactions of the American Mathematical Society, Vol. 362, No. 4 (2010), p.2089-2113
Publisher: American Mathematical Society
Date: 2010
Author/Creator: Duong, Xuan Thinh
Author/Creator: Grafakos, Loukas
Author/Creator: Yan, Lixin
Description: We obtain endpoint estimates for multilinear singular integral operators whose kernels satisfy regularity conditions significantly weaker than those of the standard Calderón-Zygmund kernels. As a consequence, we deduce endpoint L¹ ×···×L¹ to weak L¹/m estimates for the mth-order commutator of Calderón. Our results reproduce known estimates for m = 1, 2 but are new for m ≥ 3. We also explore connections between the 2nd-order higher-dimensional commutator and the bilinear Hilbert transform and deduce some new off-diagonal estimates for the former.
Description: 25 page(s)
Resource Type: journal article
Organisation: Macquarie University. Dept. of Mathematics

Identifier: http://hdl.handle.net/1959.14/88543
Identifier: ISSN:1088-6850
Identifier: mq-rm-2009008883
Language: eng
Rights: Copyright 2010 American Mathematical Society. First published in Transactions of the American Mathematical Society, Vol.362, No. 4, published by the American Mathematical Society. The original article can be found at http://www.ams.org/journals/tran/
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