This is an announcement for the paper "Nikol'skii-type inequalities for rearrangement invariant spaces" by Ostrovsky E. Sirota L. Abstract: In this paper we generalize the classical Nikol'skii inequality on the many popular classes pairs of rearrangement invariant (r.i.) spaces and construct some examples in order to show the exactness of our estimations. Archive classification: math.FA Mathematics Subject Classification: 60G17 The source file(s), Nik14_4.tex: 40903 bytes, is(are) stored in gzipped form as 0804.2311.gz with size 14kb. The corresponding postcript file has gzipped size 85kb. 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/0804.2311 or http://arXiv.org/abs/0804.2311 or by email in unzipped form by transmitting an empty message with subject line uget 0804.2311 or in gzipped form by using subject line get 0804.2311 to: math@arXiv.org.