Hankel operators induced by radial Bekolle-Bonami weights on Bergman spaces
Journal article, 2019

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.

Bergman space

doubling weight

Bekolle-Bonami weight

Bergman projection

Hankel operator

Author

Jose Angel Pelaez

University of Malaga

Antti Perälä

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Jouni Raettyae

University of Eastern Finland

Mathematische Zeitschrift

0025-5874 (ISSN) 1432-8232 (eISSN)

Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

DOI

10.1007/s00209-019-02412-8

More information

Latest update

12/6/2019