| L~p( [0, 1])-characterizations of multi-knot piecewise linear spectral sequences |
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| 作者姓名： | LIAN Qiaofang CHENG Linfeng and YAN Dunyan |
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| 作者单位： | Department of Mathematics，Beijing Jiaotong University，Beijing 100044，China; Department of Mathematics，China University of Mining and Technology，Xuzhou 221008，China; School of Information Science and Engineering，Graduate University of Chinese Academy of Sciences，Beijing 100080，China |
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| 基金项目： | 中国科学院资助项目;中国科学院基金 |
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| 摘 要： | There exists a class of new orthonormal basis for L2(0, 1]), whose exponential parts are multi-knot piecewisf 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
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Lp([0,1])-characterizations of multi-knot piecewise linear spectral sequences |
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| LIAN Qiaofang,CHENG Linfeng,and YAN Dunyan.L~p( [0, 1])-characterizations of multi-knot piecewise linear spectral sequences[J].Progress in Natural Science,2006,16(7). |
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| Authors: | LIAN Qiaofang CHENG Linfeng YAN Dunyan |
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| Abstract: | 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 L p( 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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| Keywords: | exponential bases multi-knot piecewise linear spectral sequences unconditional bases |
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