26 citations · 52 across the 26 of their papers we have counts for
6 papers · 1 filter
Carleson Conditions for Weights: The quantitative small constant case
Simon Bortz, Moritz Egert, Olli Saari
We investigate the small constant case of a characterization of weights due to Fefferman, Kenig and Pipher. In their work, Fefferman, Kenig and Pipher bound the logarith…
Elliptic measures for Dahlberg-Kenig-Pipher operators: Asymptotically optimal estimates
Simon Bortz, Tatiana Toro, Zihui Zhao
Questions concerning quantitative and asymptotic properties of the elliptic measure corresponding to a uniformly elliptic divergence form operator have been the focus of recent stu…
Carleson measure estimates for caloric functions and parabolic uniformly rectifiable sets
Simon Bortz, John Hoffman, Steve Hofmann +2
Let be a parabolic uniformly rectifiable set. We prove that every bounded solution to $$\partial_tu- Δu=0, \quad \text{in} \quad \mathbb R^{n+1}\set…
Parabolic Singular Integrals with Nonhomogeneous Kernels
Simon Bortz, John Hoffman, Steve Hofmann +2
We establish boundedness of all "nice" parabolic singular integrals on "Good Parabolic Graphs", aka {\em regular} Lip(1,1/2) graphs. The novelty here is that we include non-h…
Corona Decompositions for Parabolic Uniformly Rectifiable Sets
Simon Bortz, John Hoffman, Steve Hofmann +2
We prove that parabolic uniformly rectifiable sets admit (bilateral) corona decompositions with respect to regular Lip(1,1/2) graphs. Together with our previous work, this allows u…
On Big Pieces approximations of parabolic hypersurfaces
Simon Bortz, John Hoffman, Steve Hofmann +2
Let be a closed subset of which is parabolic Ahlfors-David regular and assume that satisfies a 2-sided corkscrew condition. Assume, in addition, that $Σ…