Abstract
The paper deals with the space consisting of classes of real measurable functions on with finite integral . If , then the space can be made into a Banach space with the norm . The inequality , which is an analogue of the first Jackson theorem, is shown to hold for the finite Fourier-Haar series , provided that the variable exponent satisfies the condition . Here, is the modulus of continuity in defined in terms of Steklov functions. If the function lies in the Sobolev space with variable exponent , it is shown that . Methods for estimating the deviation for at a given point are also examined. The value of is calculated in the case when , where .Bibliography: 17 titles.
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