Abstract of a paper by Tuomas Hytonen and Lutz Weis
This is an announcement for the paper "The Banach space-valued BMO, Carleson's condition, and paraproducts" by Tuomas Hytonen and Lutz Weis. Abstract: We define a scale of L^q Carleson norms, all of which characterize the membership of a function in BMO. The phenomenon is analogous to the John-Nirenberg inequality, but on the level of Carleson measures. The classical Carleson condition corresponds to the L^2 case in our theory. The result is applied to give a new proof for the L^p-boundedness of paraproducts with a BMO symbol. A novel feature of the argument is that all p are covered at once in a completely interpolation-free manner. This is achieved by using the L^1 Carleson norm, and indicates the usefulness of this notion. Our approach is chosen so that all these results extend in a natural way to the case of X-valued functions, where X is a Banach space with the UMD property. Archive classification: math.FA Mathematics Subject Classification: 42B35; 42B20; 42B25; 46E40 Remarks: 14 pages, submitted The source file(s), carleson.tex: 56068 bytes, is(are) stored in gzipped form as 0811.3333.gz with size 16kb. The corresponding postcript file has gzipped size 106kb. Submitted from: tuomas.hytonen@helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.3333 or http://arXiv.org/abs/0811.3333 or by email in unzipped form by transmitting an empty message with subject line uget 0811.3333 or in gzipped form by using subject line get 0811.3333 to: math@arXiv.org.
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