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Title: A modulation invariant Carleson embedding theorem outside local L^2
The article arXiv:1309.0945 by Do and Thiele develops a theory of Carleson embeddings in outer Lp spaces for the wave packet transform of functions in L^p, in the 2≤p≤∞ range referred to as local L^2. In this article, we formulate a suitable extension of this theory to exponents 1<2, answering a question posed in arXiv:1309.0945. The proof of our main embedding theorem involves a refined multi-frequency Calder\'on-Zygmund decomposition. We apply our embedding theorem to recover the full known range of Lp estimates for the bilinear Hilbert transforms without reducing to discrete model sums or appealing to generalized restricted weak-type interpolation.  more » « less
Award ID(s):
1500449
PAR ID:
10017331
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal d’analyse mathématique
ISSN:
1565-8538
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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