Acta mathematica scientia, Series B >
BOUNDEDNESS OF CALDERÓN-ZYGMUND OPERATORS ON BESOV SPACES AND ITS APPLICATION
Received date: 2008-09-23
Online published: 2010-07-20
Supported by
Sponsored by the NSF of South-Central University for Nationalities (YZZ08004) and NNSF of China (10871209)
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
Bp0, 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 Bp0, q(1≤p, q≤ ∞) . However, the proof is quite different from the previous one.
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 . DOI: 10.1016/S0252-9602(10)60129-4
[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
/
| 〈 |
|
〉 |