HARMONIC CONJUGATES OF WEIGHTED HARMONIC BERGMAN FUNCTIONS ON HALF-SPACES

Title & Authors
HARMONIC CONJUGATES OF WEIGHTED HARMONIC BERGMAN FUNCTIONS ON HALF-SPACES
Nam, Kye-Sook; Yi, Heung-Su;

Abstract
On the setting of the upper half-space of the Euclidean space $\small{R^{n}}$, we show that to each weighted harmonic Bergman function $\small{u\;\epsilon\;b^p_{\alpha}}$, there corresponds a unique conjugate system ($\small{upsilon_1}$,…, $\small{upsilon_{n-1}}$) of u satisfying $\small{upsilon_j{\epsilon}\;b^p_{\alpha}}$ with an appropriate norm bound.
Keywords
harmonic Bergman function;harmonic conjugates;weighted Bergman kernel;fractional derivative;upper half-space;
Language
English
Cited by
1.
LIPSCHITZ TYPE CHARACTERIZATIONS OF HARMONIC BERGMAN SPACES,;

대한수학회보, 2013. vol.50. 4, pp.1277-1288
1.
On Toeplitz Operators on the Weighted Harmonic Bergman Space on the Upper Half-Plane, Complex Analysis and Operator Theory, 2015, 9, 1, 139
2.
LIPSCHITZ TYPE CHARACTERIZATIONS OF HARMONIC BERGMAN SPACES, Bulletin of the Korean Mathematical Society, 2013, 50, 4, 1277
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