Abstract
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 L p , Carleson-Hunt theorem on almost everywhere convergence, Littlewood-Paley theorem and Poisson summation formula related to these bases.. * Supported by National Natural Science Foundation of China (Grant No. 10371122) ad the President Foundation of Graduate School of the Chinese Academy of Sciences (Grant No. yzjj200505)
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