“Hardy's Inequality”的概念、定义、习题解题方法及翻译-数学辞典

单词

Hardy's Inequality

释义

Hardy's Inequality

Let be a Nonnegative Sequence and a Nonnegative integrable Function. Define

(1)

and

(2)

and take

. For sums,

(3)

(unless all

), and for integrals,

(4)

(unless

is identically 0).

References

Hardy, G. H.; Littlewood, J. E.; and Pólya, G. Inequalities, 2nd ed. Cambridge, England: Cambridge University Press, pp. 239-243, 1988.

Mitrinovic, D. S.; Pecaric, J. E.; and Fink, A. M. Inequalities Involving Functions and Their Integrals and Derivatives. New York: Kluwer, 1991.

Opic, B. and Kufner, A. Hardy-Type Inequalities. Essex, England: Longman, 1990.

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