| Lp(［0,1］)-characterizations of multi-knot piecewise linear spectral sequences |
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| 作者姓名： | LIAN Qiaofang CHENG Linfeng YAN Dunyan |
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| 作者单位： | 1. Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China; 2. Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, China; 3. School of Information Science and Engineering, Graduate University of Chinese Academy of Sciences, Beijing 100080, China |
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| 摘 要： | There exists a class of new orthonormal basis for L2(［0,1］), whose exponential parts are multi-knot piecewise linear functions called spectral sequences. In this paper, we show that these bases constitute bases, but not unconditional bases, for Lp(［0,1］) with 1＜p＜∞, p≠2. In addition, we give the corresponding convergence theorem in Lp, Carleson-Hunt theorem on almost everywhere convergence, Littlewood-Paley theorem and Poisson summation formula related to these bases.
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| 关 键 词： | exponential bases multi-knot piecewise linear spectral sequences unconditional bases. |
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