Smoothness and derivatives of functions in \(H^ p(B^ n)\) spaces. (Russian) Zbl 0649.32004

Storozhenko, Eh. A.

Vestn. Mosk. Univ., Ser. I 1988, No. 4, 13-16 (1988).

By making use of suitable k-modules of continuity connected with some subsets of the group of unitary operators in \({\mathbb{C}}^ n\) it is investigated the connection between behaviour of certain derivatives (radial and orthogonal to \(O_ z\) ones) and smoothness of boundary values of \(H^ p\)-functions \((0<p\leq \infty)\) in the unit ball of \({\mathbb{C}}^ n\).

Reviewer: T.Tonev

MSC:

32A35	\(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
32A40	Boundary behavior of holomorphic functions of several complex variables
41A17	Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)

Keywords:

\(H^ p\)-functions in \({bbfC}^ n\); modulus of continuity; Haar measure; derivatives