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Young's inequality for integral operators

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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

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Assume that and are measurable spaces, is measurable and are such that . If

for all

and

for all

then [1]

Particular cases

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Convolution kernel

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If and , then the inequality becomes Young's convolution inequality.

See also

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Young's inequality for products

Notes

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  1. ^ Theorem 0.3.1 in: C. D. Sogge, Fourier integral in classical analysis, Cambridge University Press, 1993. ISBN 0-521-43464-5