26 citations · 52 across the 26 of their papers we have counts for
13 papers · 1 filter
Big Pieces of Regular Parabolic (bi-)Lipschitz Images is Equivalent to Parabolic Uniform Rectifiability
Simon Bortz, Matthew Hyde, Mason Sharp
We define the notion of regular parabolic (bi-)Lipschitz images as the parabolic (bi-)Lipschitz maps from -dimensional space time which, up to translation, fix the variable…
Weighted Sobolev Inequalities via the Meyers--Ziemer Framework: Measures, Isoperimetric Inequalities, and Endpoint Estimates
Simon Bortz, Kabe Moen, Andrea Olivo +2
We establish a new global endpoint Sobolev inequality for measures that extends the classical theorem of Meyers-Ziemer by placing a maximal function on the right-hand side. This re…
Weighted Bounded Variation Revisited
Simon Bortz, Matthew Gossett, Joseph Kasel +1
In this article, we investigate the theory of weighted functions of bounded variation (BV), as introduced by Baldi [Ba01]. Depending on the theorem, we impose lower semicontinuity…
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…
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…
Coronizations and big pieces in metric spaces
Simon Bortz, John Hoffman, Steve Hofmann +2
We prove that coronizations with respect to arbitrary d-regular sets (not necessarily graphs) imply big pieces squared of these (approximating) sets. This is known (and due to Davi…
Sobolev contractivity of gradient flow maximal functions
Simon Bortz, Moritz Egert, Olli Saari
We prove that the energy dissipation property of gradient flows extends to the semigroup maximal operators in various settings. In particular, we show that the vertical maximal fun…
Two Phase Free Boundary Problem for Poisson Kernels
Simon Bortz, Max Engelstein, Max Goering +2
We provide a potential theoretic characterization of vanishing chord-arc domains under minimal assumptions. In particular we show that, if a domain has Ahlfors regular boundary, th…
Reifenberg Flatness and Oscillation of the Unit Normal Vector
Simon Bortz, Max Engelstein
We show (under mild topological assumptions) that small oscillation of the unit normal vector implies Reifenberg flatness. We then apply this observation to the study of chord-arc…
Non-local Gehring lemmas in spaces of homogeneous type and applications
Pascal Auscher, Simon Bortz, Moritz Egert +1
We prove a self-improving property for reverse H{ö}lder inequalities with non-local right hand side. We attempt to cover all the most important situations that one encounters when…
Rectifiability, interior approximation and Harmonic Measure
Murat Akman, Simon Bortz, Steve Hofmann +1
We prove a structure theorem for any -rectifiable set , , satisfying a weak version of the lower ADR condition, and having locally finite $H^n…
Harmonic measure and approximation of uniformly rectifiable sets
Simon Bortz, Steve Hofmann
Let , , be a uniformly rectifiable set of dimension . We show that has big pieces of boundaries of a class of domains which satisfy a 2-si…
A Singular Integral approach to a Two Phase Free Boundary Problem
Simon Bortz, Steve Hofmann
We present an alternative proof of a result of Kenig and Toro, which states that if is a two sided NTA domain, with Ahlfors-David regular boundary, and…