Bounded holomorphic functions and maps with some boundary behavior
نویسندگان
چکیده
منابع مشابه
Boundary Values of Bounded Holomorphic Functions of Several Variables
A typical result (consequence of Theorem 1) is that if such a function tends to a limit X as x—»x° from inside an open cone with vertex at x°, then it tends "on the average" to X as x—>x° from inside any open cone with vertex at x°. In particular, if such a function tends to limits in each of two open cones with a common vertex, these limits must be equal; for n = l (when the cones are half-lin...
متن کاملHolomorphic Diffusions and Boundary Behavior of Harmonic Functions
Cornell University We study a family of differential operators Lα α ≥ 0 in the unit ball D of Cn with n ≥ 2 that generalize the classical Laplacian, α = 0, and the conformal Laplacian, α = 1/2 (that is, the Laplace–Beltrami operator for Bergman metric in D). Using the diffusion processes associated with these (degenerate) differential operators, the boundary behavior of Lα-harmonic functions is...
متن کاملBounded Holomorphic Functions on Bounded Symmetric Domains
Let D be a bounded homogeneous domain in C , and let A denote the open unit disk. If z e D and /: D —► A is holomorphic, then ß/(z) is defined as the maximum ratio \Vz(f)x\/Hz(x, 3c)1/2 , where x is a nonzero vector in C and Hz is the Bergman metric on D . The number ßf(z) represents the maximum dilation of / at z . The set consisting of all ß/(z), for z e D and /: D —► A holomorphic, is known ...
متن کاملWeak Topologies on the Bounded Holomorphic Functions
Let G be a region in the complex plane such that there is a nonconstant bounded holomorphic function on G, and denote the algebra of all such functions by BH{G). Let H^{G) denote the Banach algebra that arises when BH{G) is endowed with the supremum norm. In the case where G is the unit disc D, H*>(G) has been extensively studied, mostly by a real-variables analysis of the radial boundary value...
متن کاملSome notes on harmonic and holomorphic functions
These notes are concerned with harmonic and holomorphic functions on Euclidean spaces, where “holomorphic” refers to ordinary complex analysis in dimension 2 and generalizations using quaternions and Clifford algebras in higher dimensions. Among the principal themes are weak solutions, the mean-value property, and subharmonicity.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2003
ISSN: 0022-247X
DOI: 10.1016/s0022-247x(03)00471-2