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

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