26 citations · 138 across the 26 of their papers we have counts for
27 papers
The parabolic Dini- condition and absolute continuity of surface and caloric measure
Simon Bortz, Moritz Egert, Sandra Ferris +1
We show if is the graph of a parabolic Lipschitz function, then parabolic surface measure of is absolutely continuous with respect to its caloric meas…
Domains with globally exponentially integrable parabolic forward-in-time BMO
Kim Myyryläinen, Tuomas Oikari, Olli Saari
We characterize those open sets of the space time in which parabolic forward-in-time BMO functions are in a certain forward-in-time exponential integrability class. The characteriz…
A stability result for parabolic measures of operators with singular drifts
Simon Bortz, Moritz Egert, Olli Saari
We study the operator \[ \partial_t - \text{div} A \nabla + B \cdot \nabla \] in parabolic upper-half-space, where is an elliptic matrix satisfying an oscillation condition and…
Uniform bounds for bilinear symbols with linear K-quasiconformally embedded singularity
Marco Fraccaroli, Olli Saari, Christoph Thiele
We prove bounds in the strict local range for trilinear Fourier multiplier forms with a -dimensional singular subspace. Given a fixed parameter …
Phase space localizing operators
Marco Fraccaroli, Olli Saari, Christoph Thiele
We construct phase space localizing operators in all dimensions. These are frequency localized variants of the conditional expectation operator related to a dyadic stopping time. O…
local smoothing estimates for the wave equation via -broad Fourier restriction
David Beltran, Olli Saari
We explore the connection between -broad Fourier restriction estimates and sharp regularity local smoothing estimates for the solutions of the wave equation in $\mathb…
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…
Construction of a right inverse for the divergence in non-cylindrical time dependent domains
Olli Saari, Sebastian Schwarzacher
We construct a stable right inverse for the divergence operator in non-cylindrical domains in space-time. The domains are assumed to be Hölder regular in space and evolve continuou…
Paraproducts for bilinear multipliers associated with convex sets
Olli Saari, Christoph Thiele
We prove bounds in the local range for exotic paraproducts motivated by bilinear multipliers associated with convex sets. One result assumes an exponential boundary curve.…
Note on time-regularity for weak solutions to parabolic systems of p-Laplace type
Simon Bortz, Moritz Egert, Olli Saari
We show that local weak solutions to parabolic systems of p-Laplace type are H{ö}lder continuous in time with values in a spatial Lebesgue space and H{ö}lder continuous on almost e…
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…
A reverse Hölder inequality for the gradient of solutions to Trudinger's equation
Olli Saari, Sebastian Schwarzacher
We provide a higher integrability result for the gradient of positive solutions to Trudinger's equation (also known as the doubly non-linear equation) for the range $p\in [2,\infty…
Weak differentiability for fractional maximal functions of general functions on domains
João P. G. Ramos, Olli Saari, Julian Weigt
Let be bounded a domain. We prove under certain structural assumptions that the fractional maximal operator relative to maps …
The Brunn-Minkowski inequality and a Minkowski problem for -harmonic Green's function
Murat Akman, John Lewis, Olli Saari +1
In this article we study two classical problems in convex geometry associated to -harmonic PDEs, quasi-linear elliptic PDEs whose structure is modeled on the -Lapla…
Regularity of fractional maximal functions through Fourier multipliers
David Beltran, João Pedro Ramos, Olli Saari
We prove endpoint bounds for derivatives of fractional maximal functions with either smooth convolution kernel or lacunary set of radii in dimensions . We also show that…
Regularity of maximal functions on Hardy-Sobolev spaces
Carlos Pérez, Tiago Picon, Olli Saari +1
We prove that maximal operators of convolution type associated to smooth kernels are bounded in the homogeneous Hardy-Sobolev spaces when $1/p < 1+1/d…
Non-local self-improving properties: A functional analytic approach
Pascal Auscher, Simon Bortz, Moritz Egert +1
A functional analytic approach to obtaining self-improving properties of solutions to linear non-local elliptic equations is presented. It yields conceptually simple and very short…
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…
On regularity of weak solutions to linear parabolic systems with measurable coefficients
Pascal Auscher, Simon Bortz, Moritz Egert +1
We establish a new regularity property for weak solutions of parabolic systems with coefficients depending measurably on time as well as on all spatial variables. Namely, weak solu…
Lipschitz linearization of the maximal hyperbolic cross multiplier
Olli Saari, Christoph Thiele
We study the linearized maximal operator associated with dilates of the hyperbolic cross multiplier in dimension two. Assuming a Lipschitz condition and a lower bound on the linear…
Poincaré inequalities for the maximal function
Olli Saari
We study generalized Poincaré inequalities. We prove that if a function satisfies a suitable inequality of Poincaré type, then the Hardy-Littlewood maximal function also obeys a me…
Parabolic BMO and the forward-in-time maximal operator
Olli Saari
We study if the parabolic forward-in-time maximal operator is bounded on parabolic BMO. It turns out that for non-negative functions the answer is positive, but the behaviour of si…
Sharp inequalities for one-sided Muckenhoupt weights
Paul A. Hagelstein, Ioannis Parissis, Olli Saari
Let denote the class of one-sided Muckenhoupt weights, namely all the weights for which for some , where $\mathsf M^+…
Characterizations of interior polar sets for the degenerate p-parabolic equation
Benny Avelin, Olli Saari
This paper deals with different characterizations of sets of nonlinear parabolic capacity zero, with respect to the parabolic p-Laplace equation. Specifically we prove that certain…