This is an announcement for the paper "General Hormander and Mikhlin conditions for multipliers of Besov spaces" by Rishad Shahmurov. Abstract: Here a new condition for the geometry of Banach spaces is introduced and the operator--valued Fourier multiplier theorems in weighted Besov spaces are obtained. Particularly, connections between the geometry of Banach spaces and Hormander-Mikhlin conditions are established. As an application of main results the regularity properties of degenerate elliptic differential operator equations are investigated. Archive classification: math.FA math.CA Mathematics Subject Classification: 34G10, 35J25, 35J70 Remarks: 16 The source file(s), FMTWeightedB.tex: 57462 bytes, is(are) stored in gzipped form as 0811.1350.gz with size 14kb. The corresponding postcript file has gzipped size 101kb. Submitted from: shahmurov@hotmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.1350 or http://arXiv.org/abs/0811.1350 or by email in unzipped form by transmitting an empty message with subject line uget 0811.1350 or in gzipped form by using subject line get 0811.1350 to: math@arXiv.org.