Geodesic
Maximal functions and smoothness spaces in $L_{p}(ℝ^{d})
Studia Mathematica, Tome 128 (1998) no. 3, pp. 219-241

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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

G. C. Kyriazis 1

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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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