Exact order of the Lebesgue constants of hyperbolic partial sums of multiple Fourier series
The estimates for the speed of growth of the norms of the operators \(H^ N_{\alpha}: f(x)\to \sum_{| m^{\alpha}| \leq N}c_ m(f)e^{im\cdot x}\) as \(N\to \infty\) and the exact order of the quantity \(\sup_{f}\| f-H^ N_{\alpha}\|\) for the classes of functions having bounded mixed derivative are obtained.
hyperbolic partial sums of continuous periodic functions of several variables
functions having bounded mixed derivative
scientific article; zbMATH DE number 3981770