On the means of Fourier integrals and Bernstein inequality in the two-weighted setting

The norm estimation problem for Cesaro and Abel-Poisson operators acting from L-w(p)(R) to L-v(q)(R) where 1 < p <= q < infinity was investigated. These results were generalized to the multidimensional case and applied to obtain generalizations of the Bernstein inequality for integral functions of finite degree of one and several variables.