Hardy's constants-functionals in inequalities with additional summands

R. V. Makarov^a, R. G. Nasibullin<sup>a

a</sup> Kazan (Volga Region) Federal University

Abstract: Weighted Hardy-type inequalities with additional terms are considered. Weight functions depend on the distance function to the boundary of the domain and on the Bessel function. We prove one-dimensional inequalities and their spatial analogs in the $L_1$- and $L_p$-cases. As a consequence, we obtain bounds for the strong and weak Hardy constants.

Keywords: Hardy's inequality, distance function, inner radius, additional term, Bessel function, Lamb equation.

UDC: 517.5+517.923

MSC: 35R30

Received: 21.10.2024
Revised: 09.11.2024

DOI: 10.4213/mzm14346

 English version: Mathematical Notes, 2025, 117:5, 786–804

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