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Two-weighted inequalities for the derivatives of holomorphic functions and Carleson measures on the unit ball

Published online by Cambridge University Press:  22 January 2016

Hyeonbae Kang  and
Hyungwoon Koo
Hyeonbae Kang
Affiliation:
Department of Mathematics, Seoul National University, Seoul, 151-742, Korea, hkang@math.snu.ac.kr
Hyungwoon Koo
Affiliation:
Department of Mathematics, Hankuk University of Foreign Studies, Yongin, Kyungki-Do, 449-791, Korea, koohw@maincc.hufs.ac.kr
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Abstract

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We characterize those positive measure µ’s 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.

Keywords

32A1032A3632A3526A33
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 158 , December 2000 , pp. 107 - 131
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

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