[unknown]

G. Kyriazis

Studia Mathematica (1998)

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

Abstract

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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 p α ( 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 p α ( ℝ d ) spaces in terms of the coefficients of wavelet decompositions.

How to cite

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Kyriazis, 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

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  1. [BS] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, New York, 1988. Zbl0647.46057
  2. [CS] A. Calderón, and R. Scott, Sobolev type inequalities for p>0, Studia Math. 62 (1978), 75-92. Zbl0399.46031
  3. [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
  4. [D] I. Daubechies, Ten Lectures on Wavelets, SIAM, 1992. Zbl0776.42018
  5. [DP] R. DeVore and V. Popov, Interpolation of Besov spaces, Trans. Amer. Math. Soc. 305 (1988), 397-414. Zbl0646.46030
  6. [DS] R. DeVore and R. Sharpley, Maximal functions measuring smoothness, Mem. Amer. Math. Soc. 293 (1984). Zbl0529.42005
  7. [DY] R. DeVore and X. Yu, Degree of adaptive approximation, Math. Comp. 55 (1990), 625-635. Zbl0723.41015
  8. [K] G. Kyriazis, Approximation of distribution spaces by means of kernel operators, J. Fourier Anal. Appl. 2 (1996), 261-286. Zbl0893.46030
  9. [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
  10. [M] Y. Meyer, Ondelettes et Opérateurs I: Ondelettes, Hermann 1990. Zbl0694.41037
  11. [T] H. Triebel, Theory of Function Spaces II, Birkhäuser, Basel, 1992. Zbl0763.46025

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