TY - JOUR
T1 - Moment vanishing properties of harmonic Bergman functions
AU - Choe, Boo Rim
AU - Koo, Hyungwoon
AU - Yi, Heungsu
N1 - Funding Information:
✩ This research is supported in part by KOSEF(2000-1-10100-001-3) and the Research Grant of Kwangwoon University in 2003. * Corresponding author. E-mail addresses: cbr@korea.ac.kr (B.R. Choe), koohw@korea.ac.kr (H. Koo), hsyi@math.kwangwoon.ac.kr (H. Yi).
PY - 2004/8/15
Y1 - 2004/8/15
N2 - We show that Poisson integrals belonging to certain weighted harmonic Bergman spaces bδp on the upper half-space must have the moment vanishing properties. As an application, we show that b0p, p≥1, contains a dense subspace whose members have the horizontal moment vanishing properties. Also, we derive related weighted norm inequalities for Poisson integrals. As a consequence, we obtain a characterization for Poisson integrals of continuous functions with compact support in order to belong to bδp.
AB - We show that Poisson integrals belonging to certain weighted harmonic Bergman spaces bδp on the upper half-space must have the moment vanishing properties. As an application, we show that b0p, p≥1, contains a dense subspace whose members have the horizontal moment vanishing properties. Also, we derive related weighted norm inequalities for Poisson integrals. As a consequence, we obtain a characterization for Poisson integrals of continuous functions with compact support in order to belong to bδp.
KW - Half-space
KW - Moment vanishing properties
KW - Weighted harmonic Bergman functions
UR - http://www.scopus.com/inward/record.url?scp=3442893800&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=3442893800&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2003.11.005
DO - 10.1016/j.jmaa.2003.11.005
M3 - Article
AN - SCOPUS:3442893800
VL - 296
SP - 365
EP - 381
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 2
ER -