A lower bound for the spectrum of a one-dimensional pseudo-differential operator
Published online by Cambridge University Press: 24 October 2008
Extract
In a 1928 paper [1], Hardy and Littlewood published the following inequality which is valid for all non-negative measurable functions ƒ and g on ( − ∞, ∞):
where 1 < p, q < ∞, 0 < λ < 1, l/p + 1/q + λ = 2 and Cλp, q depends only on λ, p, q; ‖ƒ‖p and ‖g‖q are the Lp and Lq norms of ƒ and g respectively. See also p. 288 of the monograph [2] by Hardy, Littlewood and Pólya for a discussion of this inequality and related matters.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 2 , March 1988 , pp. 317 - 320
- Copyright
- Copyright © Cambridge Philosophical Society 1988
References
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