Abstract

We present Battle–Lemarié wavelet systems of natural orders. Our main result is a decomposition theorem in Besov and Triebel–Lizorkin spaces with local Muckenhoupt weights, which is formulated in terms of bases generated by systems of such a type. The Battle–Lemarié wavelets are splines and suit very well the study of integration operators.

中文翻译：

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加权函数空间中的样条小波分解

摘要

我们介绍自然阶的Battle–Lemarié小波系统。我们的主要结果是在Besov和Triebel–Lizorkin空间中具有局部Muckenhoupt权重的分解定理，该定理是根据此类系统生成的基数来表示的。Battle–Lemarié小波是样条曲线，非常适合集成算子的研究。