Abstract
SynopsisIn 1979 Copson proved the following analogue of the Hardy-Littlewood inequality: if is a sequence of real numbers such that are convergent, where Δan = an+1 – an and Δ2an = Δ(Δan), then is convergent and the constant 4 being best possible. Equality occurs if and only if an = 0 for all n. In this paper we give a result that extends Copson's result to inequalities of the formwhere Mxn =–Δ(pn_l Δxn_l)+qnxn (n = 0, 1, …). The validity of such an inequality and the best possible value of the constant K are determined in terms of the analogue of the Titchmarsh-Weyl m-function for the difference equation Mxn = λwnxn (n = 0, 1, …).
Publisher
Cambridge University Press (CUP)
Reference10 articles.
1. On an extension to an integro-differential inequality of Hardy, Littlewood and Pólya;Everitt;Proc. Roy. Soc. Edinburgh Sect. A,1971
2. Norm inequalities involving derivatives
3. On the spectrum of ordinary second-order differential operators;Chaudhuri;Proc. Roy. Soc. Edinburgh Sect. A,1968
4. Spectral theory for pairs of differential operators
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10 articles.
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