This is an announcement for the paper "On the relation of Carleson's embedding and the maximal theorem in the context of Banach space geometry" by Tuomas Hyt"onen and Mikko Kemppainen.

Abstract: Hyt"onen, McIntosh and Portal (J. Funct. Anal., 2008) proved two vector-valued generalizations of the classical Carleson embedding theorem, both of them requiring the boundedness of a new vector-valued maximal operator, and the other one also the type p property of the underlying Banach space as an assumption. We show that these conditions are also necessary for the respective embedding theorems, thereby obtaining new equivalences between analytic and geometric properties of Banach spaces.

Archive classification: math.FA

Mathematics Subject Classification: 42B25 (Primary) 46E40 (Secondary)

Remarks: 10 pages

The source file(s), carleson.bbl: 2240 bytes

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1002.2876

or

http://arXiv.org/abs/1002.2876

or by email in unzipped form by transmitting an empty message with subject line

uget 1002.2876

or in gzipped form by using subject line

get 1002.2876

to: math@arXiv.org.