HARMONIC CONJUGATES OF WEIGHTED HARMONIC BERGMAN FUNCTIONS ON HALF-SPACES

Abstract

On the setting of the upper half-space of the Euclidean space $R^{n}$, we show that to each weighted harmonic Bergman function $u\;\epsilon\;b^p_{\alpha}$, there corresponds a unique conjugate system ($upsilon$_1,…, $upsilon_{n-1}$) of u satisfying $upsilon_j{\epsilon}\;b^p_{\alpha}$ with an appropriate norm bound.

Keywords

• harmonic Bergman function;
• harmonic conjugates;
• weighted Bergman kernel;
• fractional derivative;
• upper half-space