A characterization for the boundedness of geometric mean operator

Authors
Jain, P Singh, AP
Citation
P. Jain et Ap. Singh, A characterization for the boundedness of geometric mean operator, APPL MATH L, 13(8), 2000, pp. 63-67
Citations number
5
Categorie Soggetti
Mathematics
Journal title
APPLIED MATHEMATICS LETTERS
ISSN journal
08939659 → ACNP
Volume
13
Issue
8
Year of publication
2000
Pages
63 - 67
Database
ISI
SICI code
0893-9659(200011)13:8<63:ACFTBO>2.0.ZU;2-3
Abstract
We give a characterization for the geometric mean inequality (integral (infinity)(0)[exp((xk+1)/(k+1)integral (x)(0)tklnf(t)dt)](q)u(x)) (1/q)less than or equal toC(integral (infinity)(0)f(p)(x)v(x)dx)(1/p) to hold for the case 0 < q < p less than or equal to infinity, p > 1, where f is positive a.e. on (0, infinity), and C > 0 independent of f. (C) 2000 Elsevier Science Ltd. All rights reserved.