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Orders of orthoprojection diameters of classes of periodic functions of one and several variables. (Russian) Zbl 0659.42008
Let \(x^{(k)}(t)\), \(t\in R\), be the derivative of fractional order k in the sense of formal differentiation of the Fourier series of a \(2\pi\)- periodic function x(t), and let \(\tilde W^ k_ p=\{x:\) \(\| x^{(k)}\|_ p\leq 1\}\). Let \(1<p^ i<\infty\), \(k^ i\in R\) for \(i=1,2,...,m\). The order of the orthoprojective diameter \(d^{\perp}_ N(\cap^{m}_{i=1}\tilde W^{k^ i}_{p^ i},L_ q)\) is established. The results are generalized also to the multidimensional case.
Reviewer: J.Musielak

42A75 Classical almost periodic functions, mean periodic functions
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems