# [unknown]

Studia Mathematica (1998)

- Volume: 128, Issue: 3, page 219-241
- ISSN: 0039-3223

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topKyriazis, G.. "null." Studia Mathematica 128.3 (1998): 219-241. <http://eudml.org/doc/216484>.

@article{Kyriazis1998,

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.},

author = {Kyriazis, G.},

journal = {Studia Mathematica},

keywords = {maximal functions; approximation by operators; wavelets; smoothness spaces},

language = {eng},

number = {3},

pages = {219-241},

url = {http://eudml.org/doc/216484},

volume = {128},

year = {1998},

}

TY - JOUR

AU - Kyriazis, G.

JO - Studia Mathematica

PY - 1998

VL - 128

IS - 3

SP - 219

EP - 241

AB - 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.

LA - eng

KW - maximal functions; approximation by operators; wavelets; smoothness spaces

UR - http://eudml.org/doc/216484

ER -

## References

top- [BS] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, New York, 1988. Zbl0647.46057
- [CS] A. Calderón, and R. Scott, Sobolev type inequalities for p>0, Studia Math. 62 (1978), 75-92. Zbl0399.46031
- [CDF] A. Cohen, I. Daubechies and J.-C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math. 45 (1992), 485-560. Zbl0776.42020
- [D] I. Daubechies, Ten Lectures on Wavelets, SIAM, 1992. Zbl0776.42018
- [DP] R. DeVore and V. Popov, Interpolation of Besov spaces, Trans. Amer. Math. Soc. 305 (1988), 397-414. Zbl0646.46030
- [DS] R. DeVore and R. Sharpley, Maximal functions measuring smoothness, Mem. Amer. Math. Soc. 293 (1984). Zbl0529.42005
- [DY] R. DeVore and X. Yu, Degree of adaptive approximation, Math. Comp. 55 (1990), 625-635. Zbl0723.41015
- [K] G. Kyriazis, Approximation of distribution spaces by means of kernel operators, J. Fourier Anal. Appl. 2 (1996), 261-286. Zbl0893.46030
- [LM] P. G. Lemarié and G. Malgouyres, Support des fonctions de base dans une analyse multi-résolution, C. R. Acad. Sci. Paris 313 (1991), 377-380. Zbl0759.42019
- [M] Y. Meyer, Ondelettes et Opérateurs I: Ondelettes, Hermann 1990. Zbl0694.41037
- [T] H. Triebel, Theory of Function Spaces II, Birkhäuser, Basel, 1992. Zbl0763.46025

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