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

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
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