Maximal functions and smoothness spaces in $L_{p}(ℝ^{d})
Volume 128 / 1998
Studia Mathematica 128 (1998), 219-241
DOI: 10.4064/sm-128-3-219-241
Abstract
We study smoothness spaces generated by maximal functions related to the local approximation errors of integral operators. It turns out that in certain cases these smoothness classes coincide with the spaces $C^α_p(ℝ^d)$, 0 < p≤∞, introduced by DeVore and Sharpley [DS] by means of the so-called sharp maximal functions of Calderón and Scott. As an application we characterize the $C^α_p(ℝ^d)$ spaces in terms of the coefficients of wavelet decompositions.
