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[edit]

If and are measurable spaces, if and , if

and

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]

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