Geodesic
Whitney type inequality, pointwise version
Yu. A. Brudnyi1 ; I. E. Gopengauz2
1 Department of Mathematics Technion Haifa, 32000, Israel
2 Department of Mathematics National Research Technical University (MISA) Moscow, 119049, Russia
Studia Mathematica, Tome 214 (2013) no. 2, pp. 167-194

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $\mu $-differences, a generalization of the $k$th 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.
DOI : 10.4064/sm214-2-5
Keywords: main result paper estimates asymptotic behavior local polynomial approximation functions point via behavior differences generalization kth difference result applied prove several extend classical results pointwise differentiability functions including marcinkiewicz zygmunds nbsp weiss theorems particular present solution problem posed marcinkiewicz zygmund

Yu. A. Brudnyi 1 ; I. E. Gopengauz 2

1 Department of Mathematics Technion Haifa, 32000, Israel
2 Department of Mathematics National Research Technical University (MISA) Moscow, 119049, Russia 
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Yu. A. Brudnyi; I. E. Gopengauz. Whitney type inequality, pointwise version. Studia Mathematica, Tome 214 (2013) no. 2, pp. 167-194. doi: 10.4064/sm214-2-5

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