Browse > Article
http://dx.doi.org/10.4134/JKMS.2013.50.1.189

HOLOMORPHIC MEAN LIPSCHITZ FUNCTIONS ON THE UNIT BALL OF ℂn  

Kwon, Ern Gun (Department of Mathematics Education Andong National University)
Cho, Hong Rae (Department of Mathematics Pusan National University)
Koo, Hyungwoon (Department of Mathematics Korea University)
Publication Information
Journal of the Korean Mathematical Society / v.50, no.1, 2013 , pp. 189-202 More about this Journal
Abstract
On the unit ball of $\mathbb{C}^n$, the space of those holomorphic functions satisfying the mean Lipschitz condition $${\int}_0^1\;{\omega}_p(t,f)^q\frac{dt}{t^1+{\alpha}q}\;<\;{\infty}$$ is characterized by integral growth conditions of the tangential derivatives as well as the radial derivatives, where ${\omega}_p(t,f)$ denotes the $L^p$ modulus of continuity defined in terms of the unitary transformations of $\mathbb{C}^n$.
Keywords
mean Lipschitz condition; Besov space; mean modulus of continuity;
Citations & Related Records
연도 인용수 순위
  • Reference
1 P. Ahern and J. Bruna, Maximal and area integral characterizations of Hardy-Sobolev spaces in the unit ball of $C^{n}$, Rev. Mat. Iberoam. 4 (1988), no. 1, 123-153.
2 P. Ahern and W. Cohn, Besov spaces, Sobolev spaces, and Cauchy integrals, Michigan Math. J. 39 (1992), no. 2, 239-261.   DOI
3 N. Arcozzi, R. Rochberg, and E. Sawyer, Carleson measures and interpolating sequences for Besov spaces on complex balls, Mem. Amer. Math. Soc. 182 (2006), no. 859, 1-163.
4 P. L. Duren, Theory of Hp Spaces, Academic Press, New York, 1970.
5 K. M. Dyakonov, Besov spaces and outer functions, Michigan Math. J. 45 (1998), no. 1, 143-157.   DOI
6 G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals II, Math. Z. 34 (1932), no. 1, 403-439.   DOI
7 M. Jevtic and M. Pavlovic, On M-harmonic Bloch space, Proc. Amer. Math. Soc. 123 (1995), no. 5, 1385-1392.
8 H. T. Kaptanoglu, Carleson measures for Besov spaces on the ball with applications, J. Funct. Anal. 250 (2007), no. 2, 483-520.   DOI   ScienceOn
9 M. Pavlovic, Lipschitz spaces and spaces of harmonic functions in the unit disc, Michigan Math. J. 35 (1988), no. 2, 301-311.   DOI
10 M. Pavlovic, On the moduli of continuity of Hp functions with 0 < p < 1, Proc. Edinb. Math. Soc. (2) 35 (1992), no. 1, 89-100.   DOI
11 Ch. Pommerenke, Boundary Behavior of Conformal Maps, Springer-Verlag, 1992.
12 E. M. Stein, Singular Integrals and Differentiability Properties of functions, Princeton University Press, New Jersey, 1970.