Whitney type inequality, pointwise version
Yu. A. Brudnyi ; I. E. Gopengauz
Studia Mathematica, Tome 215 (2013), p. 167-194 / Harvested from The Polish Digital Mathematics Library
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The main result of the paper estimates the asymptotic behavior of local polynomial approximation for Lp 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 Lp 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.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:286255 
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Yu. A. Brudnyi; I. E. Gopengauz. Whitney type inequality, pointwise version. Studia Mathematica, Tome 215 (2013) pp. 167-194. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-2-5/