Bernstein Type Inequalities for Quasipolynomials Original Research Article

We prove a Bernstein type inequality for multivariate quasipolynomials and apply it to carry out the following results. (1) The evaluation of the uniform norm for a quasipolynomial on a convex body V⊂Rn by that on a measurable subset of V. (2) The estimate of the BMO-norm for a quasipolynomial in terms of its degree and exponential type. (3) The reverse Hölder inequality with a dimensionless constant.