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

• Autorzy: G. C. Kyriazis
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

maximal functions; approximation by operators; wavelets; smoothness spaces

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 42B25: Maximal functions, Littlewood-Paley theory
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 41A63: Multidimensional problems (should also be assigned at least one other classification number in this section)
• 41A35: Approximation by operators (in particular, by integral operators)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 128
• Numer: 3
• Strony: 219-241

Daty

wydano

1998

otrzymano

1996-10-07

poprawiono

1997-05-20

Twórcy

autor

G. C. Kyriazis

• Department of Mathematics and Statistics, University of Cyprus, P.O. Box 537, Nicosia, Cyprus

Bibliografia

• [BS] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, New York, 1988.
• [CS] A. Calderón, and R. Scott, Sobolev type inequalities for p>0, Studia Math. 62 (1978), 75-92.
• [CDF] A. Cohen, I. Daubechies and J.-C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math. 45 (1992), 485-560.
• [D] I. Daubechies, Ten Lectures on Wavelets, SIAM, 1992.
• [DP] R. DeVore and V. Popov, Interpolation of Besov spaces, Trans. Amer. Math. Soc. 305 (1988), 397-414.
• [DS] R. DeVore and R. Sharpley, Maximal functions measuring smoothness, Mem. Amer. Math. Soc. 293 (1984).
• [DY] R. DeVore and X. Yu, Degree of adaptive approximation, Math. Comp. 55 (1990), 625-635.
• [K] G. Kyriazis, Approximation of distribution spaces by means of kernel operators, J. Fourier Anal. Appl. 2 (1996), 261-286.
• [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.
• [M] Y. Meyer, Ondelettes et Opérateurs I: Ondelettes, Hermann 1990.
• [T] H. Triebel, Theory of Function Spaces II, Birkhäuser, Basel, 1992.