BOUNDEDNESS OF CALDERÓN-ZYGMUND OPERATORS ON BESOV SPACES AND ITS APPLICATION

doi:10.1016/S0252-9602(10)60129-4

Abstract

Abstract:

In this article, the author introduces a class of non-convolution Calderón-Zygmund operators whose kernels are certain sums involving the products of Meyer wavelets and their convolutions. The boundedness on Besov spaces
B_p^{0, q}(1≤p, q≤ ∞) is also obtained. Moreover, as an application, the author gives a brief proof of the known result that Hörmander condition can ensure the boundedness of convolution-type Calderón-Zygmund operators on Besov spaces B_p^0, ^q(1≤p, q≤ ∞) . However, the proof is quite different from the previous one.

Key words: Calderón-Zygmund operators, Besov space Meyer wavelet, Hörmander condition

CLC Number:

42B20

Cite this article

YANG Zhan-Ying. BOUNDEDNESS OF CALDERÓN-ZYGMUND OPERATORS ON BESOV SPACES AND ITS APPLICATION[J].Acta mathematica scientia,Series B, 2010, 30(4): 1338-1346.

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URL: http://121.43.60.238/sxwlxbB/EN/10.1016/S0252-9602(10)60129-4

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References

[1] Coifman R, Meyer Y. Au delàdes Opérateurs Pseudo-differentiels. Paris: Soc Math de France (Astèrisque 57), 1978

[2] Journé J L. Calderón-Zygmund Operators, Pseudo-differential Operators and the Cauchy Integral of
Calderón. Lecture Notes in Math(994). Berlin: Springer-Verlag, 1983

[3] Meyer Y. Ondelettes et Opérateurs. Paris: Hermann, 1990

[4] Cheng M D, Deng D G, Long, R L. Real Analysis. Beijing: High Eduction Press,1993 (Chinese)

[5] David G, Journe J L. A boundedness criterion for generalized Calderón-Zygmund operators. Ann of Math, 1984, 120(2): 371--397

[6] Beylkin G, Coifman R, Rokhlin V. Fast wavelet transforms and numerical algorithms I. Comm Pure Appl Math, 1991, 44(2): 141--183

[7] Meyer Y, Yang Q X. Continuity of Calderón-Zygmund operators on Besov spaces or Triebel-Lizorkin spaces. Anal and Appl, 2008, 6(1): 51--81

[8] Yang Z Y, Yang Q X. Convolution-type Calderón-Zygmund operators and approximation. Acta Math Sinica (Ser A), 2008, 51(6): 1061--1072

[9] Yang Z Y, Yang Q X. A note on convolution-type Calderón-Zygmund operators. Acta Mathematica Scientia (Ser B), 2009, 29(5): 1341--1350

[10] Peng L Z, Yang Q X. Predual spaces for Q spaces. Acta Mathematica Scientia (Ser B), 2009, 29(2): 243--250

[11] Yang Q X, Cheng Z X, Peng L Z. Uniform characterization of function spaces by wavelets. Acta Mathematica Scientia (Ser A), 2005, 25(1): 130--144

[12] Lemarié P G. Continuité sur les espaces de Besov des opérateurs définis par des intégrales singuliéres. Ann Inst Fourier (Grenoble), 1985, 35(4): 175--187

[13] Triebel H. Theory of Function Spaces. Basel: Birkhauser Verlag, 1983

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