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Journal of Zhejiang University SCIENCE A 2002 Vol.3 No.1 P.94~99

http://doi.org/10.1631/jzus.2002.0094


Decomposition in blocks at the level of wavelet coefficients and T(1) theorem on Hardy space


Author(s):  YANG Qi-xiang

Affiliation(s):  Department of Mathematics, Wuhan University, Wuhan 430072, China

Corresponding email(s): 

Key Words:  hardy space, wavelet coefficients, blocks


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YANG Qi-xiang. Decomposition in blocks at the level of wavelet coefficients and T(1) theorem on Hardy space[J]. Journal of Zhejiang University Science A, 2002, 3(1): 94~99.

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Abstract: 
This paper deals with the establishment of T(1) theorem on hardy space H1 under condition of weak regularity. An operator or a function is identified on the basis of their wavelet coefficients which are regrouped on some blocks. The actions of each block operator (pseudo-annular operator) on each block function (atom) are exactly analyzed to establish T(1) theorem on hardy space

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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[2] Coifman,R., Weiss,G., 1977. Extensions of Hardy spaces and their use in analysis., Bull.Amer.Math.Soc., 83:569-645.

[3] David,G., Journé,J.L., 1984. A boundedness criterion for generalized Calderéon-Zygmund operators. Ann. of Math., 120:371-397.

[4] Deng,D.G. Yan,L.X. Yang,Q.X., 1998. Blocking analysis and T(1) theorem. Science in China, 8:(41):801-808.

[5] Han,Y.S., Hofman,S., 1993. T(1) theorem for Besov and Triebel-Lizorkin space. Transactions of the American Mathematical Society, 2: 337.

[6] Meyer,Y., 1985. Universidad autónoma de Madrid. (The smallest Besov space B10,1 and certains singular integral operators' continuity). Monografias de Matematicas, 4.

[7] Meyer,Y., 1990-1991. Ondelettes et op'erateurs I et II (Wavelettes and operators), Herman, Paris.

[8] Yang,Q.X., 1996. Fast algorithms for Calderéon-Zygmund singular intergral operators. Appl. and Comp. Harmonic analysis, 3: 120-126

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