Ahlfors Bers Colloquium
May
19-22, 2005
University of
Michigan
Ann Arbor, Michigan
Registration
Organizers
Dick
Canary
Juha
Heinonen
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Workshop
Abstract Detail
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Ignacio Uriarte-Tuero Helsinki University
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On Marcinkiewicz integrals and harmonic measure
Jones and Makarov gave sharp density estimates for harmonic measure using a modified version of Marcinkiewicz integrals called $\tilde I_{0}$. It was also used by Jones and Smirnov to substantially advance in the Sobolev and quasiconformal removability problems. We generalize and slightly change $\tilde I_{0}$ to make it account for different densities of sets over which to integrate, in particular giving a different proof than Jones' and Makarov's of its key properties. This should have applications to the aforementioned Sobolev and quasiconformal removability problems. | ||
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