This article may be too technical for most readers to understand.(July 2017) |
In mathematical analysis, the Young's inequality for integral operators, is a bound on the operator norm of an integral operator in terms of norms of the kernel itself.
Statement edit
Assume that and are measurable spaces, is measurable and are such that . If
- for all
and
- for all
then [1]
Particular cases edit
Convolution kernel edit
If and , then the inequality becomes Young's convolution inequality.
See also edit
Notes edit
- ^ Theorem 0.3.1 in: C. D. Sogge, Fourier integral in classical analysis, Cambridge University Press, 1993. ISBN 0-521-43464-5