Best constants for the Riesz projection

被引:69
作者
Hollenbeck, B [1 ]
Verbitsky, IE [1 ]
机构
[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA
关键词
Riesz projection; best constants; Fourier multipliers; plurisubharmonic functions; weighted LP spaces;
D O I
10.1006/jfan.2000.3616
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We prove the following inequality with a sharp constant, \\P+ f\\(Lp(T)) less than or equal to csc pi/p \\f\\(Lp(T)), f is an element of L-p(T), where 1 < p < infinity, and P+:L-p(T) --> H-p(T) is the Ricsz projection onto the Hardy spate H-p(T) on the unit circle T. (In other words, the "angle" between the analytic and to-analytic subspaces of L-p(T) equals pi/p* where p* = max (p, p/p-1).) This was conjectured in 1968 by I. Gohberg and N. Krupnik. We also prove an analogous inequality in the nonperiodic case where P(+)f = F-1 (chi(R+) Ff) is the half-line Fourier multiplier on R. Similar weighted inequalities with sharp constants for L-p(R, \x\(alpha)), -1 < alpha < p - 1, are obtained. In the multidimensional case, our results give the norm of the half-space Fourier multiplier on R-n. (C) 2000 Academic Press.
引用
收藏
页码:370 / 392
页数:23
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