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Hankel operators induced by radial Bekolle-Bonami weights on Bergman spaces

Journal article
Authors J. A. Pelaez
Antti Perälä
J. Rattya
Published in Mathematische Zeitschrift
Pages 28
ISSN 0025-5874
Publication year 2019
Published at Department of Mathematical Sciences
Pages 28
Language en
Links dx.doi.org/10.1007/s00209-019-02412...
Keywords Hankel operator, Bekolle-Bonami weight, Bergman space, Bergman, projection, doubling weight, bmo
Subject categories Mathematics

Abstract

We study big Hankel operators H-f(nu) : A(omega)(p) -> L-nu(q) generated by radial Bekolle-Bonami weights nu, when 1 < p <= q < infinity. Here the radial weight omega is assumed to satisfy a two-sided doubling condition, and A(omega)(p) denotes the corresponding weighted Bergman space. A characterization for simultaneous boundedness of H-f(nu) and H nu/f is provided in terms of a general weighted mean oscillation. Compared to the case of standard weights that was recently obtained by Pau et al. (Indiana Univ Math J 65(5):1639-1673, 2016), the respective spaces depend on the weights omega and nu in an essentially stronger sense. This makes our analysis deviate from the blueprint of this more classical setting. As a consequence of our main result, we also study the case of anti-analytic symbols.

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