Abstract
We obtain upper bounds in terms of Fourier coefficients for the best approximation by an “angle” and for norms in the metric of L p for functions of two variables defined by trigonometric series with coefficients such that \(a_{l_1 l_2 } \to 0\) as l 1 + l 2 → ∞ and
for a certain p, 1 < p < ∞.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 9, pp. 1182–1192, September, 2004.
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Kononovych, T.O. Estimation of the best approximation of periodic functions of two variables by an “angle” in the metric of L p . Ukr Math J 56, 1403–1416 (2004). https://doi.org/10.1007/s11253-005-0124-8
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DOI: https://doi.org/10.1007/s11253-005-0124-8