Volume 4 Number 1 (Jan. 2014)
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IJAPM 2014 Vol.4(1): 46-50 ISSN: 2010-362X
DOI: 10.7763/IJAPM.2014.V4.253

The Bijectivity of the Tight Frame Operators in Lebesgue Spaces

Kai-Cheng Wang, Chi-I. Yang, and Kuei-Fang Chang
Abstract—The motivation of this dissertation mainly is which affine frame wavelet systems span Lebesgue spaces have been investigated less. The technique we used is analogous to technique of Calderón-Zygmund operators, but we rely on Calderón-Zygmund decomposition theorem. We prove our main results without smoothness assumption on frame wavelets. We prove that affine tight frame wavelets span Lebesgue spaces under the condition, we also show that the affine tight frame operator extends from L2(R) to a bounded, linear and bijective operator on  Lp (R) , for 1< p < . Under such condition, the affine orthonormal basis of L2(R) is also an unconditional basis for 1< p < .

Index Terms—Bijective, frames, orthogonal basis, unconditional basis, wavelets.

Kai-Cheng Wang is with Ph.D. Program in Mechanical and Aeronautical Engineering, Feng-Chia University, 40724 Tai-Chung, Taiwan (e-mail: gtotony98@gmail.com).
Chi-I. Yang and Kuei-Fang Chang are with Department of Applied Mathematics, Feng-Chia University, 40724 Tai-Chung, Taiwan (e-mail: yesheslhamo@gmail.com, kfchang@math.fcu.edu.tw).

Cite: Kai-Cheng Wang, Chi-I. Yang, and Kuei-Fang Chang, "The Bijectivity of the Tight Frame Operators in Lebesgue Spaces," International Journal of Applied Physics and Mathematics vol. 4, no. 1, pp. 46-50, 2014.

General Information

ISSN: 2010-362X (Online)
Abbreviated Title: Int. J. Appl. Phys. Math.
Frequency: Quarterly
DOI: 10.17706/IJAPM
Editor-in-Chief: Prof. Haydar Akca 
Abstracting/ Indexing:  Index Copernicus, EI (INSPEC, IET), Chemical Abstracts Services (CAS), Nanowerk Database, Google Scholar, EBSCO, etc.
E-mail: ijapm@iap.org
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