Boundary values of bounded holomorphic functions
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...
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WD = {z => x + iy\ x Q R , y & D). The distinguished boundary of WD is the set {z = x+iy \ xÇzR, y = 0 } , i.e., just R. In this paper we consider the following problem. Let ƒ be a real function on R satisfying certain regularity conditions. What are the conditions for the existence of a holomorphic function F on WD such that ƒ is the limit of Re -Fas the variable approaches the distinguished b...
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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 ...
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The solution to (1.1) gives the value of the Bergman kernel function associated to Ω (the kernel of the operator projecting L(Ω) orthogonally onto O(Ω)) at (p, p). If n = 1, it is a classical fact that MΩ(p) is bounded, from above and below, by a constant factor times dist(p, bΩ)−2. In higher dimensions, the geometry of bΩ influences the size of MΩ(p) in non-trivial ways. A general lower bound ...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1972
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-44-4-355-358