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Whitney type inequality, pointwise version

Tom 214 / 2013

Yu. A. Brudnyi, I. E. Gopengauz Studia Mathematica 214 (2013), 167-194 MSC: Primary 26Bxx; Secondary 41A10. DOI: 10.4064/sm214-2-5

Streszczenie

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.

Autorzy

  • Yu. A. BrudnyiDepartment of Mathematics
    Technion
    Haifa, 32000, Israel
    e-mail
  • I. E. GopengauzDepartment of Mathematics
    National Research Technical University (MISA)
    Moscow, 119049, Russia
    e-mail

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