Приближение функций в $L^{p(x)}_{2\pi}$ тригонометрическими полиномами

We generalize and improve the results of A. Guven, D. Israfilov, Xh. Z. Krasniqi and T. N. Shakh-Emirov. We consider the general methods of summability of Fourier series of functions from L p(x) 2π with p (x) ≥ 1. For estimate of the error of approximation of functions by the matrix means we use a modulus of continuity constructed by the Steklov functions of the increments of considered functions without of absolute values.

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Wavelet Characterization of Local Muckenhoupt Weighted Sobolev Spaces with Variable Exponents

Izuki

Nogayama

Noi

et al. 2022

Constr Approx

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The goal of this paper is to define local weighted variable Sobolev spaces of fractional order and its chracterization by wavelet. We first consider local weighted variable Sobolev spaces by means of weak derivatives and obtain wavelet characterization for these spaces. Using the Bessel potentials, we next define local weighted variable Sobolev spaces of fractional order. We show that Sobolev spaces obtained by weak derivatives and those by the Bessel potentials coincide. We also show that local weighted variable Sobolev spaces are closed under complex interpolation. Some examples are given including the applications to weighted uniformly local Lebesgue spaces with variable exponents and periodic function spaces as a byproduct, although the exponent is constant.

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Приближение функций в $L^{p(x)}_{2\pi}$ тригонометрическими полиномами

Cited by 15 publications

References 24 publications

Approximation by Matrix Transforms in Weighted Lebesgue Spaces with Variable Exponent

Approximation by Matrix Transforms in Weighted Lebesgue Spaces with Variable Exponent

Trigonometric Approximation of Functions from $$L_{2\pi }^{p(x)}$$

Wavelet Characterization of Local Muckenhoupt Weighted Sobolev Spaces with Variable Exponents

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