GROWTH NORM ESTIMATES FOR ¯∂ ON CONVEX DOMAINS

Title & Authors
GROWTH NORM ESTIMATES FOR ¯∂ ON CONVEX DOMAINS
Cho, Hong-Rae; Kwon, Ern-Gun;

Abstract
We consider the growth norm of a measurable function f defined by defined by $\small{{\parallel}f{\parallel}-\sigma=ess\;sup\{\delta_D(z)^\sigma{\mid}f(z)\mid:z{\in}D\}}$, where $\small{\delta_D(z)}$ denote the distance from z to $\small{{\partial}D}$. We prove some kind of optimal growth norm estimates for a on convex domains.
Keywords
growth norm estimates for $\small{\={\partial}}$;Lipschitz space;convex domains;
Language
English
Cited by
References
1.
H. Ahn and H. R. Cho, Zero sets of holomorphic functions in the Nevanlinna type class on convex domains in $C^2$, Japan. J. Math. (N.S.) 28 (2002), no. 2, 245-260

2.
F. Beatrous, Estimates for derivatives of holomorphic functions in pseudoconvex domains, Math. Z. 191 (1986), 91-116

3.
F. Beatrous and J. Burbea, Holomorphic Sobolev spaces on the ball, Dissertationes Math. 256 (1989), 1-57

4.
B. Berndtsson and M. Andersson, Henkin-Ramirez formulas with weight factors, Ann. Inst. Fourier 32 (1982), 91-110

5.
H. R. Cho, Estimates on the mean growth of Hp functions in convex domains of finite type, Proc. Amer. Math. Soc. 131 (2003), no. 8, 2393-2398

6.
H. R. Cho and E. G. Kwon, Embedding of Hardy spaces into weighted Bergman spaces in bounded domains with $C^2$ boundary, Illinois J. Math. 48 (2004), 747-757

7.
P. L. Duren, Theory of $H^p$ spaces, Academic Press, New York, 1970

8.
J. C. Polking, The Cauchy-Riemann equations in convex domains, Proc. Symp. Pure Math. 52 (1991), 309-322

9.
M. Range, Holomorphic functions and integral representations in several complex variables, Springer Verlag, Berlin, 1986

10.
M. Range, On Holder and BMO estimates for $\bar{a}$ on convex domains in $C^2$, Journal Geom. Anal. 2 (1992), no. 4, 575-584