Bounds for the operator norms of some Nörlund matrices期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Bounds for the operator norms of some Nörlund matrices

Authors:	P D Johnson Jr R N Mohapatra Jr David Ross Jr

Institution:	Department of Discrete and Statistical Sciences 120 Math Annex Auburn University, Alabama 36849-5307 ; Department of Mathematics University of Central Florida Orlando, Florida 32816-6690 David Ross Jr. ; Department of Mathematics Embry Riddle Aeronautical University Daytona Beach, Florida 32114

Abstract:	Suppose $(p_n)_{n \geq 0}$ is a non-increasing sequence of non-negative numbers with , $P_n = \sum _{j=0}^n p_j$ , $n = 0, 1 \dots$ , and $A = A(p_n) = (a_{nk})$ is the lower triangular matrix defined by $a_{nk} = p_{n-k} / P_n$ , $0 \leq k \leq n$ , and $a_{nk} = 0$ , . We show that the operator norm of as a linear operator on $\ell _p$ is no greater than , for $1 < p < \infty$ ; this generalizes, yet again, Hardy's inequality for sequences, and simplifies and improves, in this special case, more generally applicable results of D. Borwein, Cass, and Kratz. When the tend to a positive limit, the operator norm of on $\ell _p$ is exactly . We also give some cases when the operator norm of on $\ell _p$ is less than .

Keywords:

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文