Abstract
We establish an elementary convolution inequality which appears to be novel although it extends and complements a famous old result of W.H. Young. In the course of the proof we are led to a simple interpolation result which has applications in measure theory.
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References
Beckenbach, E.F. and Bellman, R. (1971). Inequalities, Springer-Verlag, Berlin, Heidelberg, New York.
Brown, G. Some inequalities that arise in measure theory, preprint.
Hardy, G.H., Littlewood, J.E., and Pólya, G. (1951). Inequalities. Cambridge University Press, London.
Jessen, B. (1931). Om Uligheder imellem Potensmiddelvaerdier. Mat Tidsskrift, B No. 1. D.H. Oberlin, The size of sum sets, II. preprint.
Young, W.H. (1913). On the determination of the summability of a function by means of its Fourier constants. Proc. London Math. Soc. Proc. London Math2 (12), 71–88.
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© 1989 Springer-Verlag New York, Inc.
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Brown, G., Shepp, L. (1989). A Convolution Inequality. In: Gleser, L.J., Perlman, M.D., Press, S.J., Sampson, A.R. (eds) Contributions to Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3678-8_4
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DOI: https://doi.org/10.1007/978-1-4612-3678-8_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8200-6
Online ISBN: 978-1-4612-3678-8
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