L~p([0,1])-characterizations of multi-knot piecewise linear spectral sequences

摘要

There exists a class of new orthonormal basis for L~2 ([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.