Sharp estimates for the identity minus Hardy operator on the cone of decreasing functions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

Sharp estimates for the identity minus Hardy operator on the cone of decreasing functions

Authors:	Natan Kruglyak Eric Setterqvist

Affiliation:	Department of Mathematics, Luleå University of Technology, SE-971 87, Luleå, Sweden ; Global Sun Engineering AB, Aurorum Science Park 2, SE-97775 Luleå, Sweden

Abstract:	It is shown that if we restrict the identity minus Hardy operator on the cone of nonnegative decreasing functions in $L^{p}$ , then we have the sharp estimate $displaystyle leftVert (I-H)frightVert _{L^p}leq frac{1}{(p-1)^{frac{1}{p}}}leftVert frightVert _{L^p}$ for In other words, $displaystyle leftVert f^{*}-f^ rightVert _{L^p}leq frac{1}{(p-1)^{frac{1}{p}}} leftVert frightVert _{L^p}$ for each and each integer . It is also shown, via a connection between the operator and Laguerre functions, that $displaystyle Vert(1-alpha) I+alpha (I-H)Vert _{L^2to L^2}=Vert I-alpha HVert _{L^2to L^2}=1$ for all .

Keywords:	The Hardy operator cone of decreasing functions sharp estimates

	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》下载全文