Whitney type inequality, pointwise version

Yu. A. Brudnyi, and I. E. Gopengauz. "Whitney type inequality, pointwise version." Studia Mathematica 214.2 (2013): 167-194. <http://eudml.org/doc/286255>.

@article{Yu2013,
abstract = {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.},
author = {Yu. A. Brudnyi, I. E. Gopengauz},
journal = {Studia Mathematica},
keywords = {$\mu $-difference; local polynomial approximation; Taylor classes; ($k$; $p$)-differential},
language = {eng},
number = {2},
pages = {167-194},
title = {Whitney type inequality, pointwise version},
url = {http://eudml.org/doc/286255},
volume = {214},
year = {2013},
}

TY - JOUR
AU - Yu. A. Brudnyi
AU - I. E. Gopengauz
TI - Whitney type inequality, pointwise version
JO - Studia Mathematica
PY - 2013
VL - 214
IS - 2
SP - 167
EP - 194
AB - 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.
LA - eng
KW - $\mu $-difference; local polynomial approximation; Taylor classes; ($k$; $p$)-differential
UR - http://eudml.org/doc/286255
ER -