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A brief survey of Nigel Kalton's work on interpolation and related topics
This is the third of a series of papers surveying some small part of the
remarkable work of our friend and colleague Nigel Kalton. We have written it as
part of a tribute to his memory. It does not contain new results. This time,
rather than concentrating on one particular paper, we attempt to give a general
overview of Nigel's many contributions to the theory of interpolation of Banach
spaces, and also, significantly, quasi-Banach spaces.Comment: 11 page
Bilinear Forms on the Dirichlet Space
Let be the classical Dirichlet space, the Hilbert space of
holomorphic functions on the disk. Given a holomorphic symbol function we
define the associated Hankel type bilinear form, initially for polynomials f
and g, by , where we are looking at the
inner product in the space .
We let the norm of denotes its norm as a bilinear map from
to the complex numbers. We say a function is
in the space if the measure
is a Carleson measure for and norm by
Our main result is is bounded if and only if and Comment: v1: 29 page
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