Characterizations of A2 matrix power weights

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:453

Article

Bickel, Kelly¹  Lunceford, Katherine¹  Mukhtar, Naba¹ 

[1] Bucknell Univ, Dept Math, 701 Moore Ave, Lewisburg, PA 17837 USA

关键词: A(2) matrix weights;    Power functions;   

DOI  :  10.1016/j.jmaa.2017.04.035

来源: Elsevier

【 摘 要 】

In the scalar setting, the power functions vertical bar x vertical bar(gamma), for -1 < gamma < 1, are the canonical examples of A(2) weights. In this paper, we study two types of power functions in the matrix setting, with the goal of obtaining canonical examples of A(2) matrix weights. We first study Type 1 matrix power functions, which are n x n matrix functions whose entries are of the form a vertical bar x vertical bar(gamma). Our main result characterizes when these power functions are A(2) matrix weights and has two extensions to Type 1 power functions of several variables. We also study Type 2 matrix power functions, which are n x n matrix functions whose eigenvalues are of the form a vertical bar x vertical bar(gamma). We find necessary conditions for these to be A(2) matrix weights and give an example showing that even nice functions of this form can fail to be A(2) matrix weights. (C) 2017 Published by Elsevier Inc.

【 授权许可】

Free