多元小波为L^p(1

Multiwavelets as unconditional bases in L^p(1 我的收藏 名 称： 注 释：

作　　者：潘雅丽[1] 

机构地区：[1]山东科技大学理学院,山东青岛266590

出　　处：《西北师范大学学报（自然科学版）》2013年第3期20-24,共5页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11101120);山东科技大学"春蕾计划"项目(2010AZZ078)

摘　　要：正交小波基是小波分析理论中的重要问题,它对信号处理和压缩、信号去噪有重要的应用价值.L2(R2)空间的正交小波基可以由多尺度分析构造.本文定义了算子Tω,证明了它是是弱(1,1)的,并用此结果及Marcinkiewicz插值定理得到小波基构成了Lp(R2)空间的无条件基,其中多元小波有某些充分弱的衰减条件.作为辅助结果,证明了正交映射Pj和正交余映射Qj在算子Tw下满足一些不等式.Orthonormal wavelet basis is an important issue in wavelet and has an important application on image processing and compression, signal denoising etc. The orthonormal wavelet basis for L^2 （R^2） can be formulated by MRA. In this paper, an operator Tw is defined, which is uniformly in w of week type （1, 1）. By this result and Marcinkiewicz interpolation theorem, it is proved that the wavelet bases are unconditional bases in L^p （R^2）, where the wavelets with some weak sufficient decay properties. Some inequalities of the orthonormal projection Pj and the complementary orthonormal projection Qj restricted to the operator Tw are discussed.

关 键 词：多尺度分析 小波 无条件基 

分 类 号：O177.1[理学—数学]