Holomorphic almost periodic functions on coverings of complex manifolds.
Whitney type inequality, pointwise version
The main result of the paper estimates the asymptotic behavior of local polynomial approximation for functions at a point via the behavior of μ-differences, a generalization of the kth difference. The result is applied to prove several new and extend classical results on pointwise differentiability of functions including Marcinkiewicz-Zygmund’s and M. Weiss’ theorems. In particular, we present a solution of the problem posed in the 30s by Marcinkiewicz and Zygmund.
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