This is an announcement for the paper "On the Rademacher maximal function" by Mikko Kemppainen. Abstract: This paper studies a new maximal operator introduced by Hyt\"onen, McIntosh and Portal in 2008 for functions taking values in a Banach space. The L^p-boundedness of this operator depends on the range space; certain requirements on type and cotype are present for instance. The original Euclidean definition of the maximal function is generalized to sigma-finite measure spaces with filtrations and the L^p-boundedness is shown not to depend on the underlying measure space or the filtration. Martingale techniques are applied to prove that a weak type inequality is sufficient for L^p-boundedness and also to provide a characterization by concave functions. Archive classification: math.FA Mathematics Subject Classification: 46E40 (Primary); 42B25 (Secondary) Remarks: 22 pages, 4 figures The source file(s), RMF.bbl: 4575 bytes RMF.tex: 148459 bytes averages.pdf: 1054 bytes filtrations.pdf: 1394 bytes mart11.pdf: 1111 bytes mart33.pdf: 1082 bytes, is(are) stored in gzipped form as 0912.3358.tar.gz with size 39kb. The corresponding postcript file has gzipped size . Submitted from: mikko.k.kemppainen@helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.3358 or http://arXiv.org/abs/0912.3358 or by email in unzipped form by transmitting an empty message with subject line uget 0912.3358 or in gzipped form by using subject line get 0912.3358 to: math@arXiv.org.