Maximal functions and smoothness spaces in $L_{p}(ℝ^{d})

Tom 128 / 1998

G. C. Kyriazis Studia Mathematica 128 (1998), 219-241 DOI: 10.4064/sm-128-3-219-241


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.


  • G. C. Kyriazis

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