Abstract. We investigate the approximation properties of the partial sums of the Fourier series and prove some direct and inverse theorems for approximation by polynomials in weighted Orlicz spaces. In particular we obtain a constructive characterization of the generalized Lipschitz classes in these spaces.
In this work, the inverse problem of approximation theory in the variable exponent Smirnov classes of analytic functions, defined on the Jordan domains with a Dinismooth boundaries, is studied. First, for this purpose, an inverse theorem in the variable exponent Lebesgue spaces of 2π periodic functions is obtained. Later, using the special linear operators, this inverse theorem to the variable exponent Smirnov classes of analytic functions is moved.
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