%0 Journal Article %A Martínez Ansemil, José María %A Aron, Richard M. %A Ponte Miramontes, María Del Socorro %T Entire unbounded functions on Banach spaces with a monotone Schauder basis. %D 2012 %@ 1222-9016 %U https://hdl.handle.net/20.500.14352/43946 %X In this work we investigate the inverse approximation problems in the Lebesgue and Smirnov spaces with weights satisfying the so-called Muckenhoupt's Ap condition in terms of the -th mean modulus of smoothness, > 0. We obtain a converse theorem of trigonometric approximation in the weighted Lebesgue spaces and obtain some converse theorems of algebraic polynomial approximation in the weighted Smirnov spaces. %~