This is an announcement for the paper "On the upper and lower estimates of norms in variable exponent spaces" by Tengiz Kopaliani, Nino Samashvili and Shalva Zviadadze. Abstract: In the present paper we investigate some geometrical properties of the norms in Banach function spaces. Particularly there is shown that if exponent $1/p(\cdot)$ belongs to $BLO^{1/\log}$ then for the norm of corresponding variable exponent Lebesgue space we have the following lower estimate $$\left\|\sum \chi_{Q}\|f\chi_{Q}\|_{p(\cdot)}/\|\chi_{Q}\|_{p(\cdot)}\right\|_{p(\cdot)}\leq C\|f\|_{p(\cdot)}$$ where $\{Q\}$ defines disjoint partition of $[0;1]$. Also we have constructed variable exponent Lebesgue space with above property which does not possess following upper estimation $$\|f\|_{p(\cdot)}\leq C\left\|\sum \chi_{Q}\|f\chi_{Q}\|_{p(\cdot)}/\|\chi_{Q}\|_{p(\cdot)}\right\|_{p(\cdot)}. $$ Archive classification: math.FA Mathematics Subject Classification: 42B35, 42B20, 46B45, 42B25 Remarks: 13 pages Submitted from: sh.zviadadze@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.3461 or http://arXiv.org/abs/1411.3461