On estimate of deviation of biharmonic Poisson integral from its boundary values in terms of modulus of continuity
Arsen M. Shutovskyi, Vitalii V. Pryt · Ukrainian Mathematical Bulletin · 2024
The paper is devoted to the study of the approximation properties of the biharmonic Poisson integral for the upper half-plane. The problem of approximating functions by biharmonic Poisson operators for the upper half-plane in the metric space $\displaystyle{L}_{p}\left(-\infty,+\infty\right)$ is considered. The main result of the paper is based on the representation of the integral kernel of the biharmonic Poisson integral obtained by applying the parameterization approach. It was found that the considered integral kernel belongs to the class of delta-shaped kernels. An upper bound is obtained for the approximation of functions by biharmonic Poisson operators in terms of the first-order modulus of continuity.