Geodesic
Supplements of Hölder's Inequality
Canadian journal of mathematics, Tome 36 (1984) no. 3, pp. 405-420

Voir la notice de l'article provenant de la source Cambridge University Press

Given vectors and (or functions f(x) and g(x)) we define the Hölder Quotient Hpq by 1 or in case of functions by 2 Here ‖·‖p and ‖·‖q are the usual Lp and Lq norms. We assume throughout that If p and q are both greater than one then they are positive but if we allow p and q to be less than one then one of them must be positive and the other one must be negative. This may cause a problem if for example, some value ai is zero and p is negative. In this case we use the convention that and 
Barnes, David C. Supplements of Hölder's Inequality. Canadian journal of mathematics, Tome 36 (1984) no. 3, pp. 405-420. doi: 10.4153/CJM-1984-025-5
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[1] 1. Hardy, G. H., Littlewood, J. E. and Pólya, G., Inequalities (Cambridge Univ. Press, London, 1964). Google Scholar

[2] 2. Mitrinović, D. S., Analytic inequalities (Springer-Verlag, New York, 1970). Google Scholar | DOI

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