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Function Spaces Related to the Dirichlet Space
Nicola Arcozzi, Richard Rochberg, Eric Sawyer +1
We present results about spaces of holomorphic functions associated to the classical Dirichlet space. The spaces we consider have roles similar to the roles of and in…
Bilinear Forms on the Dirichlet Space
Nicola Arcozzi, Richard Rochberg, Eric Sawyer +1
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…
The Corona Theorem for the Drury-Arveson Hardy space and other holomorphic Besov-Sobolev spaces on the unit ball in
Serban Costea, Eric T. Sawyer, Brett D. Wick
We prove that the multiplier algebra of the Drury-Arveson Hardy space on the unit ball in has no corona in its maximal ideal space, thus generalizing t…
Astala's Conjecture on Distortion of Hausdorff Measures under Quasiconformal Maps in the Plane
Michael T. Lacey, Eric T. Sawyer, Ignacio Uriarte-Tuero
Let E be a compact set in the plane, g be a K-quasiconformal map, and let 0<t<2. Then H^t (E) = 0 implies H^{t'} (g E) = 0, for t'=[2Kt]/[2+(K-1)t]. This is a refinement of a set o…