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Whitney type inequality, pointwise version

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Brudnyi Y., Gopengauz I.

Studia Mathematica

2013

tom 214

nr 2

167-194

The main result of the paper estimates the asymptotic behavior of local polynomial approximation for $L_{p}$ 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 $L_{p}$ 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.

Ograniczanie wyników

1 Studia Mathematica

1 Brudnyi Y.

1 Gopengauz I.

1 2013

Wyniki wyszukiwania

Whitney type inequality, pointwise version