# HARMONIC CONJUGATES OF WEIGHTED HARMONIC BERGMAN FUNCTIONS ON HALF-SPACES

• Published : 2003.07.01
• 47 5

#### 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

#### References

1. Singular integrals and differentiablity of functions E.Stein
2. Trans. Amer. Math. Soc. v.348 Harmonic Bergman functions on half-spaces W.Ramey;H.Yi https://doi.org/10.1090/S0002-9947-96-01383-9
3. Weighted harmonic Bergman kernel and its applications on half-spaces H.Koo;K.S.Nam;H.Yi
4. Fourier analysis on euclidean spaces E.Stein;G.Weiss
5. Indiana Univ. Math. J. v.40 no.3 Behavior of holomorphic functions near weakly pseudoconvex boundary points F.Beatrous https://doi.org/10.1512/iumj.1991.40.40041

#### Cited by

1. On Toeplitz Operators on the Weighted Harmonic Bergman Space on the Upper Half-Plane vol.9, pp.1, 2015, https://doi.org/10.1007/s11785-014-0388-9
2. LIPSCHITZ TYPE CHARACTERIZATIONS OF HARMONIC BERGMAN SPACES vol.50, pp.4, 2013, https://doi.org/10.4134/BKMS.2013.50.4.1277