The Bergman Spaces

By H. Hedenmalm, B. Korenblum, Kehe Zhu. 2000

543 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/609ac4427cea94f8bc7d1b263f3a63caca030e5a

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In Applied Mathematics

Citations in the corpus

An equivalence for weighted integrals of an analytic function and ist derivative (2008, background): “The first known result in this area was proved by Hardy and Littlewood, for the standard weights ω(r) = (1 − r), α > −1, see Theorem 6 of [5] for a proof, [3] and [6] for references and information, and also [1, 2, 9, 11, 12, 15, 16, 17, 21] for various generalizations.”
A Paley–Wiener theorem for Bergman spaces with application to invariant subspaces (2007, background): “Since the polynomials are dense in A(2)α(D) (see for instance [3]), the monomials w with n = 0, 1, 2, .”
Small weighted Bergman spaces (2015, methodology): “As usual, we write Aα for the standard weighted Bergman space induced by the radial weight (1 − |z|2)α, where −1 < α < ∞ [26, 33, 63].”
A Hankel matrix acting on Hardy and Bergman spaces (2010, methodology): “For the theory of these spaces we refer to [DS] and [Zh].”
Carleson measures, multipliers and integration operators for spaces of Dirichlet type (2006, background): “We mention [10,17] as general references for the theory of Bergman spaces.”
Norm of the Hilbert matrix on Bergman and Hardy spaces and a theorem of Nehari type (2008, background): “For more about these spaces, the reader may consult [5] or [9].”
Sharp two-weight inequalities for singular integrals, with applications to the Hilbert transform and the Sarason conjecture (2007, background): “For more information on the Bergman spaces, see [14].”
Weighted Bergman spaces induced by rapidly incresing weights (2012, background): “Therefore the reasoning gives an alternative proof of the known characterization of q-Carlesonmeasures for the classical weighted Bergman spaceAα [29, 84].”
INTEGRABILITY OF THE DERIVATIVE OF A BLASCHKE PRODUCT (2007, background): “We refer the reader to [7], [21], and [14] for the theory of these spaces.”
GENERALIZED HILBERT OPERATORS (2012, methodology): “We refer to [5] for the theory of Hardy spaces, and to [6], [13] and [19] for Bergman spaces.”
What is a Quadrature Domain (2005, background): “In this way quadrature identities (in a wide sense) are related to Hedenmalm’s theory of contractive zero divisors [65], [30] [31].”