Young's inequality for integral operators
Appearance
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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]Young's inequality for products
Notes
[edit]- ^ Theorem 0.3.1 in: C. D. Sogge, Fourier integral in classical analysis, Cambridge University Press, 1993. ISBN 0-521-43464-5