Nonuniform Wavelet Packet Bases for the Spaces Lp(R) and H1(R)

Abstract

In this paper, we prove the results on the existence of unconditional nonuniform wavelet packet bases for the spaces L^p(R), 1 < p < ∞ and H¹(R) based on the approach similar to that of Meyer and Coifman. Certain results are obtained in this direction by assuming only that the nonuniform wavelet packets ω_n and its derivativesω'_n have a common radial decreasing L¹–majorant function.

Key words and phrases. Wavelet, nonuniform multiresolution analysis, wavelet packets, radial decreasing L¹-functions, unconditional basis.

2000 Mathematics Subject Classification. 42C40, 42C15, 46B15, 46E30