Abstract
The following result is established. Letf be a bounded function on theN-dimensional torus, andV a polyhedron in RN. Denote bySnV(f) the partial sum of ordern of the Fourier series off that is generated byV. Letp∈[1, ∞). Under some natural assumptions on∂V, for every convex sequence {nj} of integers satisfying \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\log n_j \leqq Cj^{min (1/2N,1/pN)} , C > 0,$$ \end{document} the following inequality is true: \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{...
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