On the integral representation of superbiharmonic functions
Czechoslovak Mathematical Journal (2007)
- Volume: 57, Issue: 3, page 877-883
- ISSN: 0011-4642
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topAbkar, Ali. "On the integral representation of superbiharmonic functions." Czechoslovak Mathematical Journal 57.3 (2007): 877-883. <http://eudml.org/doc/31169>.
@article{Abkar2007,
abstract = {We consider a nonnegative superbiharmonic function $w$ satisfying some growth condition near the boundary of the unit disk in the complex plane. We shall find an integral representation formula for $w$ in terms of the biharmonic Green function and a multiple of the Poisson kernel. This generalizes a Riesz-type formula already found by the author for superbihamonic functions $w$ satisfying the condition $0\le w(z)\le C(1-|z|)$ in the unit disk. As an application we shall see that the polynomials are dense in weighted Bergman spaces whose weights are superbiharmonic and satisfy the stated growth condition near the boundary.},
author = {Abkar, Ali},
journal = {Czechoslovak Mathematical Journal},
keywords = {superbiharmonic function; biharmonic Green function; weighted Bergman space; superbiharmonic function; biharmonic Green function; weighted Bergman space},
language = {eng},
number = {3},
pages = {877-883},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the integral representation of superbiharmonic functions},
url = {http://eudml.org/doc/31169},
volume = {57},
year = {2007},
}
TY - JOUR
AU - Abkar, Ali
TI - On the integral representation of superbiharmonic functions
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 3
SP - 877
EP - 883
AB - We consider a nonnegative superbiharmonic function $w$ satisfying some growth condition near the boundary of the unit disk in the complex plane. We shall find an integral representation formula for $w$ in terms of the biharmonic Green function and a multiple of the Poisson kernel. This generalizes a Riesz-type formula already found by the author for superbihamonic functions $w$ satisfying the condition $0\le w(z)\le C(1-|z|)$ in the unit disk. As an application we shall see that the polynomials are dense in weighted Bergman spaces whose weights are superbiharmonic and satisfy the stated growth condition near the boundary.
LA - eng
KW - superbiharmonic function; biharmonic Green function; weighted Bergman space; superbiharmonic function; biharmonic Green function; weighted Bergman space
UR - http://eudml.org/doc/31169
ER -
References
top- 10.1090/S0002-9939-02-06491-2, Proc. Amer. Math. Soc. 131 (2003), 155–164. (2003) Zbl1037.31002MR1929035DOI10.1090/S0002-9939-02-06491-2
- 10.1006/jfan.2001.3851, J. Func. Anal. 191 (2002), 224–240. (2002) Zbl1059.30049MR1911185DOI10.1006/jfan.2001.3851
- 10.1215/S0012-7094-94-07502-9, Duke Math. J. 75 (1994), 51–78. (1994) MR1284815DOI10.1215/S0012-7094-94-07502-9
- Banach Spaces of Analytic Functions, Dover Publications, Inc. New York, 1988. (1988) Zbl0734.46033MR1102893
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