35 citations · 168 across the 30 of their papers we have counts for
35 papers
Endpoint power weight inequalities for spherical maximal functions
Marco Fraccaroli, Juyoung Lee, Nikou Lei +2
We prove sharp estimate for spherical maximal functions. We resolve the remaining open problem for the full maximal operator for and and prove a more gen…
Formalizing Carleson's Theorem in Lean
Lars Becker, María Inés de Frutos-Fernández, Leo Diedering +11
We present the formalization of Carleson's theorem in the proof assistant Lean. This paper describes the mathematical content, organization of the project, the blueprint, and the m…
A weak Hellinger inequality for noisy Boolean channels
Polona Durcik, Marco Fraccaroli, Joris Roos
A weak form of the Hellinger conjecture of Anantharam, Bogdanov, Chakrabarti, Jayram, and Nair for the binary symmetric channel is proved: dictator functions maximize Hellinger …
A blueprint for the formalization of norm-variation of multiple ergodic averages for commuting transformations
Floris van Doorn, Polona Durcik, Joris Roos +2
This blueprint serves as a companion to a forthcoming, shorter traditional mathematical paper. The purpose of this blueprint is two-fold: first, it has served as the foundation for…
Sharp isoperimetric inequalities on the Hamming cube II: The critical exponent
Polona Durcik, Paata Ivanisvili, Joris Roos +1
A sharp isoperimetric inequality for the Hamming cube is proved at the critical exponent . This follows up on previous work, where such bounds were established for n…
Power weight inequalities for spherical maximal functions
Marco Fraccaroli, Joris Roos, Andreas Seeger
This paper is about spherical maximal functions with general dilation sets acting on functions in weighted spaces. Aside from endpoint cases, a complete description of…
Problems on spherical maximal functions
Joris Roos, Andreas Seeger
We survey old and new conjectures and results on various types of spherical maximal functions, emphasizing problems with a fractal dilation set.
A fractal local smoothing problem for the wave equation
David Beltran, Joris Roos, Alex Rutar +1
For any given set , we discuss a fractal frequency-localized version of the local smoothing estimates for the half-wave propagator with times in . A conjec…
Inner-outer factorization of analytic matrix-valued functions
Joris Roos
This is a study of inner-outer factorization for analytic matrix-valued functions focusing on representations of the factors in terms of multiplicative integrals. Included is a bri…
Spherical maximal operators with fractal sets of dilations on radial functions
David Beltran, Joris Roos, Andreas Seeger
For a given set of dilations , Lebesgue space mapping properties of the spherical maximal operator with dilations restricted to are studied when acting on radia…
Sharp isoperimetric inequalities on the Hamming cube near the critical exponent
Polona Durcik, Paata Ivanisvili, Joris Roos
An isoperimetric inequality on the Hamming cube for exponents is proved, achieving equality on any subcube. This was previously known for $β\ge \log_2(3/2)\approx 0.…
A blueprint for the formalization of Carleson's theorem on convergence of Fourier series
Lars Becker, María Inés de Frutos-Fernández, Leo Diedering +14
This paper is the blueprint underlying the Lean formalization of the proof of Carleson's classical result asserting almost everywhere convergence of Fourier series of continuous fu…
Bochner-Riesz means at the critical index: Weighted and sparse bounds
David Beltran, Joris Roos, Andreas Seeger
We consider Bochner-Riesz means on weighted spaces, at the critical index . For every -weight we obtain an extension of Vargas' weak…
A new type of superorthogonality
Philip T. Gressman, Lillian B. Pierce, Joris Roos +1
We provide a simple criterion on a family of functions that implies a square function estimate on for every even integer . This defines a new type of superorthogona…
Endpoint sparse domination for classes of multiplier transformations
David Beltran, Joris Roos, Andreas Seeger
We prove endpoint results for sparse domination of translation invariant multiscale operators. The results are formulated in terms of dilation invariant classes of Fourier multipli…
A new proof of an inequality of Bourgain
Polona Durcik, Joris Roos
The purpose of this short note is to demonstrate how some techniques from additive combinatorics recently developed by Peluse and Peluse-Prendiville can be applied to give an alter…
Spherical maximal operators on Heisenberg groups: Restricted dilation sets
Joris Roos, Andreas Seeger, Rajula Srivastava
Consider spherical means on the Heisenberg group with a codimension two incidence relation, and associated spherical local maximal functions where the dilations are restrict…
Discrete analogues of maximally modulated singular integrals of Stein-Wainger type: bounds for
Ben Krause, Joris Roos
It is proved that certain discrete analogues of maximally modulated singular integrals of Stein-Wainger type are bounded on for all . This e…
On the strict majorant property in arbitrary dimensions
Philip T. Gressman, Shaoming Guo, Lillian B. Pierce +2
In this work we study -dimensional majorant properties. We prove that a set of frequencies in satisfies the strict majorant property on for all $p…
Lebesgue space estimates for spherical maximal functions on Heisenberg groups
Joris Roos, Andreas Seeger, Rajula Srivastava
We prove estimates for local maximal operators associated with dilates of codimension two spheres in Heisenberg groups; these are sharp up to two endpoints. The result…
Pointwise convergence of certain continuous-time double ergodic averages
Michael Christ, Polona Durcik, Vjekoslav Kovač +1
We prove a.e. convergence of continuous-time quadratic averages with respect to two commuting -actions, coming from a single jointly measurable measure-preserving $\mat…
Multi-scale sparse domination
David Beltran, Joris Roos, Andreas Seeger
We prove a bilinear form sparse domination theorem that applies to many multi-scale operators beyond Calderón-Zygmund theory, and also establish necessary conditions. Among the app…
Trilinear smoothing inequalities and a variant of the triangular Hilbert transform
Michael Christ, Polona Durcik, Joris Roos
Lebesgue space inequalities are proved for a variant of the triangular Hilbert transform involving curvature. The analysis relies on a crucial trilinear smoothing inequality develo…
Spherical maximal functions and fractal dimensions of dilation sets
Joris Roos, Andreas Seeger
For the spherical mean operators in , , we consider the maximal functions , with dilation sets $E\subse…