The Approximation Numbers of Hardy-Type Operators on Trees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

The Approximation Numbers of Hardy-Type Operators on Trees

Authors:	Evans, W. D. Harris, D. J. Lang, J.

Affiliation:	School of Mathematics, Cardiff University Senghennydd Road, Cardiff CF24 4YH, evanswd{at}cardiff.ac.uk Mathematics Department, 202 Mathematical Sciences Building, University of Missouri Columbia, MO 65211, USA, langjan{at}math.missouri.edu

Abstract:	The Hardy operator T_a on a tree ${Gamma}$ is defined by Properties of T_a as a map from L^p( ${Gamma}$ ) into itselfare established for 1 $≤$ p $≤$ ${infty}$ . The main result is that, with appropriateassumptions on u and v, the approximation numbers a_n(T_a) ofT_a satisfy for a specified constant ${alpha}$ _p and 1 p < ${infty}$ . This extends results of Naimark, Newmanand Solomyak for p = 2. Hitherto, for p $!=$ 2, () was unknowneven when ${Gamma}$ is an interval. Also, upper and lower estimates forthe l^q* and weak-l^q norms of a_n(T_a) are determined. 2000 MathematicalSubject Classification: 47G10, 47B10.

Keywords:	approximation numbers asymptotic formula Hardy-type operators trees
本文献已被 Oxford 等数据库收录！