Analytic Capacity and Non-doubling Measures
Office hours: J. Garnett: MWF 10:30 in MS 7941
Grades:
Lowest possible grade is A. However, I expect written
solutions of some of the homework problems assigned in
class.
Please write all solutions in tex and submit them as
printed pdf or dvi files.
Topics:
I.
Analytic Capacity:
a) Painlev\'e Problem
b) Ahlfors functions
c) Vistushkin's Approximation Theory (in brief)
d) Duality argument
e) Calderon's theorem
f) Rectifiability, the Jones beta numbers, and Menger curvature
g) The Matilla-Melnikov-Verdera theorem
II.
Non-doubling Measures:
a)
The T(1) theorem
b) David's theorem
c) Tolsa's theorems .
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