Whitney type inequality, pointwise version

• Autorzy: Yu. A. Brudnyi , I. E. Gopengauz
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 26Bxx: Functions of several variables
• 41A10: Approximation by polynomials

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 214
• Numer: 2
• Strony: 167-194

Daty

wydano

2013

Twórcy

autor

Yu. A. Brudnyi

• Department of Mathematics, Technion, Haifa, 32000, Israel

autor

I. E. Gopengauz

• Department of Mathematics, National Research Technical University (MISA), Moscow, 119049, Russia

Identyfikatory

DOI

10.4064/sm214-2-5