Resumen de Two-Weight estimates in Lp(x) spaces with applications to Fourier series

David Eric Edmunds, Vakhtang Kokilashvili, Alexander Meskhi

• In the present paper we establish sufficient conditions governing two-weighted inequalities for Hardy-Littlewood maximal functions and Calderon-Zygmund operators in variable Lebesgue spaces. Explicit, natural examples are given of pairs of weights that satisfy these conditions.The norm summability of Fourier series and a generalization of Bernstein inequality in a two-weighted setting are proved.