## Abstract

One considers the Kontorovich-Lebedev integral transform, r>0, where\(K_{i_\tau } (\rho )\) is the Macdonald function. It is proved that, under the condition

$$g (r) = \frac{2}{{\pi ^2 r}} \int\limits_0^\infty {\tau sh} \pi \tau K_{ij} (r) \left( {\int\limits_0^\infty { g} (\rho ) K_{i\tau } (\rho ) d\rho } \right) d\tau , r > 0$$

*g*(ρ) ∈*L*_{1}, (0, ∞) ∩*L*_{p}(0, ∞),*p*∈(1, ∞), the Abel means of this integral converge to g(r) in the*L*_{p}(a, b)-norm for any finite segment [a, b] ⊂(0, ∞).## Keywords

Macdonald Function Finite Segment Abel Means
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## Literature cited

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© Plenum Publishing Corporation 1992