Two-weighted inequalities for the derivatives of holomorphic functions and Carleson measures on the unit ball. (English) Zbl 0964.32001

Kang, Hyeonbae; Koo, Hyungwoon

Nagoya Math. J. 158, 107-131 (2000).

This paper characterizes those positive measures \(\mu\) on the higher dimensional unit ball such that “two-weighted inequalities” hold for holomorphic functions and their derivatives. Characterizations are given in terms of the Carleson measure conditions.
The results of this paper also distinguish between the fractional and the tangential derivatives.

Reviewer: H.Koo (Yongin, Korea)

MSC:

32A10	Holomorphic functions of several complex variables
32A36	Bergman spaces of functions in several complex variables
32A35	\(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
26A33	Fractional derivatives and integrals

Keywords:

Carleson measure; weighted inequality; holomorphic function; radial derivative; tangential derivative