THEORY OF BERGMAN SPACES (Graduate Texts in Mathematics 199) By HAAKAN HEDENMALM, BORIS KORENBLUM and KEHE ZHU: 286 pp., £37.50, ISBN 0-387-98791-6 (Springer, New York, 2000).

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Toeplitz operators with BMO symbols and the Berezin transform (2003, background): “Toeplitz operators are one of the most widely studied classes of concrete operators.”
Multiplication operators on the Bergman space via the Hardy space of the bidisk (2009, background): “By the famous Beurling Theorem [9], the lattice of the invariant subspaces of the multiplication operator by z on the Hardy space is completely determined by inner functions.”
Weighted Bergman spaces and the integral means spectrum of conformal mappings (2004, background): “C V ] 1 7 Ju n 20 04 Weighted Bergman spaces and the integral means spectrum of conformal mappings H̊akan Hedenmalm and Serguei Shimorin at the Royal Institute of Technology, Stockholm”
Higher‐dimensional Reidemeister torsion invariants for cusped hyperbolic 3‐manifolds (2011, background): “It is well known that A(2)(DR) is a Hilbert space with respect to the following inner product (see [14]): 〈f, g〉 = ∫”
Weighted integrability of polyharmonic functions (2012, methodology): “11 of [20], which settles part (d), if we also use Hölder’s inequality to obtain the Lp statement.”