This is an announcement for the paper "Some new moment rearrangement invariant spaces; theory and applications" by Eugene Ostrovsky and Leonid Sirota. Abstract: In this article we introduce and investigate some new Banach spaces, so - called moment spaces, and consider applications to the Fourier series, singular integral operators, theory of martingales. Archive classification: Functional Analysis Mathematics Subject Classification: Primary (1991) 37B30,33K55 The source file(s), MOMSPC1.tex: 56149 bytes, is(are) stored in gzipped form as 0605732.gz with size 18kb. The corresponding postcript file has gzipped size 72kb. Submitted from: leos@post.sce.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0605732 or http://arXiv.org/abs/math.FA/0605732 or by email in unzipped form by transmitting an empty message with subject line uget 0605732 or in gzipped form by using subject line get 0605732 to: math@arXiv.org.