Maximal functions and smoothness spaces in Lp(ℝd)
Date
1998Source
Studia MathematicaVolume
128Issue
3Pages
219-241Google Scholar check
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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 Cαp (ℝd), 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 Cαp (ℝd) spaces in terms of the coefficients of wavelet decompositions.