On the Quasi-greedy Constant of the Haar Subsystems in L~1(0,1)

摘要

In this paper, we estimate the quasi-greedy constant for quasi-greedy subsystems of the Haar system in L-1(0, 1). All quasi-greedy subsystems of the Haar system are characterized in [4]. The characterization is based on the length of the chains, which is introduced in [5]. In [4], the estimate G(H) C bold /bold2H was obtainedwith H being the length of the longest chain of the subsystem. In this paper, we improve this estimate and show that H/16 G(H) 2H + 1.