M. Langer,
A general HELP inequality connected with symmetric operators,
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 462 (2006), 587–606

Abstract:
In this paper, a general HELP (Hardy–Everitt–Littlewood–Pólya) inequality is considered which is connected with a symmetric operator in a Hilbert space and abstract boundary mappings. A criterion for the validity of such an inequality in terms of the abstract Titchmarsh–Weyl function is proved and applied to Sturm–Liouville operators, difference operators, a Hamiltonian system and a block operator matrix.

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