Geodesic
Maximal functions and smoothness spaces in $L_{p}(ℝ^{d})
Studia Mathematica, Tome 128 (1998) no. 3, pp. 219-241
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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 $C^α_p(ℝ^d)$, 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.
DOI : 10.4064/sm-128-3-219-241
Keywords: maximal functions, approximation by operators, wavelets, smoothness spaces 
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G. C. Kyriazis. Maximal functions and smoothness spaces in $L_{p}(ℝ^{d}). Studia Mathematica, Tome 128 (1998) no. 3, pp. 219-241. doi: 10.4064/sm-128-3-219-241

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