A Cauchy-Schwarz type inequality for bilinear integrals on positive measures
Author:
Nils Ackermann
Journal:
Proc. Amer. Math. Soc. 133 (2005), 2647-2656
MSC (2000):
Primary 26D15; Secondary 43A35, 35J20, 60E15
DOI:
https://doi.org/10.1090/S0002-9939-05-08082-2
Published electronically:
April 15, 2005
MathSciNet review:
2146210
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: If is Borel measurable, define for
-finite positive Borel measures
on
the bilinear integral expression

We give conditions on





Our results apply to a much larger class of functions

- 1. N. Ackermann, On a periodic Schrödinger equation with nonlocal superlinear part, Math. Z. 248 (2004), no. 2, 423-443. MR 2088936
- 2. B. Buffoni, L. Jeanjean, and C.A. Stuart, Existence of a nontrivial solution to a strongly indefinite semilinear equation, Proc. Amer. Math. Soc. 119 (1993), no. 1, 179-186. MR 1145940 (93k:35086)
- 3. B. Grünbaum, Convex polytopes, With the cooperation of Victor Klee, M. A. Perles and G. C. Shephard. Pure and Applied Mathematics, Vol. 16, Interscience Publishers, John Wiley & Sons, Inc., New York, 1967. MR 0226496 (37:2085)
- 4. L. Mattner, Strict definiteness of integrals via complete monotonicity of derivatives, Trans. Amer. Math. Soc. 349 (1997), no. 8, 3321-3342. MR 1422615 (97m:26026)
- 5. Z. Sasvári, Positive definite and definitizable functions, Mathematical Topics, vol. 2, Akademie Verlag, Berlin, 1994. MR 1270018 (95c:43005)
- 6. J. Stewart, Positive definite functions and generalizations, an historical survey, Rocky Mountain J. Math. 6 (1976), no. 3, 409-434. MR 0430674 (55:3679)
- 7. C. Zong, Strange phenomena in convex and discrete geometry, Universitext, Springer-Verlag, New York, 1996. MR 1416567 (97m:52001)
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 26D15, 43A35, 35J20, 60E15
Retrieve articles in all journals with MSC (2000): 26D15, 43A35, 35J20, 60E15
Additional Information
Nils Ackermann
Affiliation:
Justus-Liebig-Universität, Mathematisches Institut, Arndtstr. 2, D-35392 Giessen, Germany
Email:
nils.ackermann@math.uni-giessen.de
DOI:
https://doi.org/10.1090/S0002-9939-05-08082-2
Keywords:
Integral inequalities,
positive definite functions,
Cauchy-Schwarz inequality
Received by editor(s):
June 18, 2003
Received by editor(s) in revised form:
April 21, 2004
Published electronically:
April 15, 2005
Communicated by:
Andreas Seeger
Article copyright:
© Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.