RT Journal Article T1 Entire unbounded functions on Banach spaces with a monotone Schauder basis. A1 Ansemil, José María M. A1 Aron, Richard M. A1 Ponte, Socorro AB 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. PB Romanian Academy SN 1222-9016 YR 2012 FD 2012 LK https://hdl.handle.net/20.500.14352/43946 UL https://hdl.handle.net/20.500.14352/43946 LA eng NO Haciyeva, E.A., Investigations of the properties of functions with quasimonotone Fourier coe cients in generalized Nikolskii-Besov spaces, Author's summary of Dissertation, Tbilisi, 1986 (in Russian).Israfilov, D.M. and Akgun, R. � , Approximation in weighted Smirnov-Orlicz classes, J. Math. Kyoto Univ., 46 (4) (2006), 755-770.Israfilov, D.M. and Guven, A., Approximation in weighted Smirnov classes, East J. Approx., 11 (1) (2005), 91-102.Ky, N.X., Moduli of mean smoothness and approximation with Ap-weights, Ann. Univ. Sci. Budapest. Sect. Math., 40 (1997), 37-48.Ky, N.X., An Alexits's lemma and its applications in approximation theory, Functions, Series, Operators (L. Leindler, F. Schipp, J. Szabados, eds.), Budapest (2002), 287-296.Taberski, R., Two indirect approximation theorems, Demonstratio Math., 9 (2) (1976), 243-255.Taberski, R., Approximation of functions possessing derivatives of positive orders, Ann. Polon. Math., 34 (1977), 13-23.Taberski, R., Diferences, moduli and derivatives of fractional orders, Comment. Math., 19 (1977), 389-400.Zygmund, A., Trigonometric series, I and II, Cambridge University Press, 1959. DS Docta Complutense RD 2 may 2024