TY - JOUR AU - Lei Qiao PY - 2014/10/25 Y2 - 2024/03/29 TI - Dirichlet Problems for Harmonic Functions in Half Spaces JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 66 IS - 10 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2228 AB - In our paper, we prove that if the positive part $u^{+}(x)$ of a harmonic function $u(x)$ in a half space satisfies the condition of slow growth, then its negative part $u^{-}(x)$ can also be dominated by a similar growth condition. Moreover, we give an integral representation of the function $u(x)$. Further, a solution of the Dirichlet problem in the half space for a rapidly growing continuous boundary function is constructed by using the generalized Poisson integral with this boundary function. ER -