Approximation in weighted rearrangement invariant Smirnov spaces

Abstract

In the present work, we investigate the approximation problems in weighted rearrangement invariant Smirnov spaces. We prove a direct theorem for polynomial approximation of functions in certain subclasses of weighted rearrangement invariant Smirnov spaces

Faber-Laurent Series in Variable Smirnov Classes

“…When p (•) = const > 1 , different versions of Theorems 1.6 and 1.8 in the classical Smirnov, Smirnov-Orlicz classes of analytic functions defined on the simple connected domains can be found in the monograph [20, chapter X] and also in [8][9][10][11][12]. In the case of variable exponent p (•) similar problems were investigated in [1,2,7,[13][14][15][16][17]22].…”

Gadjieva's conjecture, K -functionals, and some applications in weighted Lebesgue spaces

“…, and f ∈ L p γ with the Fourier series (26), then there is a function G ∈ L p γ such that the series…”