Citation
M. Cwikel et R. Kerman, ON A CONVOLUTION INEQUALITY OF SAITOH, Proceedings of the American Mathematical Society, 124(3), 1996, pp. 773-777
Citations number
6
Categorie Soggetti
Mathematics, General",Mathematics,Mathematics
Journal title
ISSN journal
00029939
Volume
124
Issue
3
Year of publication
1996
Pages
773 - 777
Database
ISI
SICI code
0002-9939(1996)124:3<773:OACIOS>2.0.ZU;2-E
Abstract
Let F-1, F-2,..., F-j,... be in the class L(loc)(R(+)) of locally inte
grable functions on R(+) = (0, infinity). Define the convolution produ
ct Pi(j=1)(m)F-j inductively by [Pi(j=1)(2)*F-j](x) = (F-1 * F-2)(x)
= integral(0)(x) F-1(y)F-2(x - y) dy and Pi(j=1)(m)F-j = [Pi(j=1)(m-1
)F-j]*F-m for m > 2. The inequality [GRAPHICS] is obtained for each p
, 1 < p < infinity. Further, the constant [(m-1)l](1-p) is shown to be
the best possible, and the nonzero extremal functions are determined.