Fejér-Riesz inequality for holomorphic functions of several complex variables
نویسندگان
چکیده
منابع مشابه
Inequalities for Holomorphic Functions of Several Complex Variables
Sharp norm-inequalities, valid for functional Hilbert spaces of holomorphic functions on the polydisk, unit ball and C" are established by using the notion of reproducing kernels. These inequalities extend earlier results of Saitoh and ours.
متن کاملOn Identical Vanishing of Holomorphic Functions in Several Complex Variables.
We will make some comment on the following recent result of J. J. Kohn. In the complex space Cn:(z1, . . . , zn) if fl, . . . , fn are holomorphic in the unit ball and have continuous boundary values on the boundary, and if on the boundary the linear combination 1fi+ + j,,f is 0, then the functions fl, . .. , f,, are identically 0. 1. We denote by D any bounded circular domain in C., by B its b...
متن کاملGlobal Holomorphic Functions in Several Noncommuting Variables
We define a free holomorphic function to be a function that is locally a bounded nc-function. We prove that free holomorphic functions are the functions that are locally uniformly approximable by free polynomials. We prove a realization formula and an OkaWeil theorem for free analytic functions.
متن کاملClasses of Holomorphic Functions of Several Variables in Circular Domains.
where ax depends only on X and nothing else. Also, for r1, r2 < 1, fo' ff(re219) f(r2e2tri) x dO -* 0 as (ri, r2) --(1, 1), and there exists a measurable function F(O) on the boundary r = e2'i0 such that, for 0 < r < 1, fol If(re2i0) F(O)lx do -0 as r -* 1. The quantity M(r) = fOIif(re ) | do is monotonely increasing in r. Using this, it is not hard to verify that Theorem 1 gives rise to the fo...
متن کاملBoundary 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 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: Tohoku Mathematical Journal
سال: 1981
ISSN: 0040-8735
DOI: 10.2748/tmj/1178229350