We establish an exact-order estimate for the deviation of partial Fourier sums of periodic functions of many variables from the classes \( B_{{p,\theta}}^{\Omega } \) in the space L p with p = 1, ∞.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 9, pp. 1204–1213, September, 2012.
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Myronyuk, V.V. Approximation of the classes \( {\boldsymbol{B}}_{{ {\boldsymbol{p}},{\boldsymbol{\theta}}}}^{\Omega } \) of periodic functions of many variables by Fourier sums in the space L p with p = 1, ∞. Ukr Math J 64, 1370–1381 (2013). https://doi.org/10.1007/s11253-013-0722-9
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DOI: https://doi.org/10.1007/s11253-013-0722-9