2 citations · 2 across the 5 of their papers we have counts for
5 papers
Julia Sets for Sequences of Monomials
Lubashan Pathirana, Carsten Lunde Petersen, Dimitris Vardakis
We study Julia sets arising from non-autonomous iteration of monomials on the Riemann sphere. We give a precise description of the Julia set associated to an arbitrary sequence of…
Matrix-weighted estimates beyond Calderón-Zygmund theory
Spyridon Kakaroumpas, Thu Hien Nguyen, Dimitris Vardakis
We investigate matrix-weighted bounds for the sublinear non-kernel operators considered by F. Bernicot, D. Frey, and S. Petermichl. We extend their result to sublinear operators ac…
The Buffon's needle problem for random planar disk-like Cantor sets
Dimitris Vardakis, Alexander Volberg
We consider a model of randomness for self-similar Cantor sets of finite and positive -Hausdorff measure. We find the sharp rate of decay of the probability that a Buffon needle…
Free boundary problems via Sakai's theorem
Dimitris Vardakis, Alexander Volberg
A Schwarz function on an open domain is a holomorphic function satisfying on , which is part of the boundary of . Sakai in 1991 gave a complete characte…
Geometry of planar curves intersecting many lines in a few points
Dimitris Vardakis, Alexander Volberg
The local Lipschitz property is shown for the graph avoiding multiple point intersection with lines directed in a given cone. The assumption is much stronger than those of Marstran…