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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

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