Spectral estimates of Cauchy's operator on Bergman space of harmonic functions.

In this paper we investigate the asymptotic behaviour of singular numbers of the operator P h C P h , where C is Cauchy's operator and P h is the orthogonal projection from L 2 ( D ) onto harmonic function subspace. We prove that s n ( P h C P h ) = O ( 1 n ) , as n → + ∞ . Moreover, we find the upper and lower asymptotic estimates, π − 1 ⩽ lim n → + ∞ ⁡ n s n ( P h C P h ) ⩽ π − 1 ( 35 + 21 2 6 ) + 7 6 . [ABSTRACT FROM AUTHOR]