Andreas Seeger

activity

20242026

collaborators

7 papers

math.CA2026

Endpoint power weight inequalities for spherical maximal functions

Marco Fraccaroli, Juyoung Lee, Nikou Lei +2

We prove sharp $L^{p} (∣ x ∣^{α})$ estimate for spherical maximal functions. We resolve the remaining open problem for the full maximal operator for $α = 1 - d$ and $p < 2$ and prove a more gen…

math.CA2026

Mollified disc multipliers

Anthony Carbery, Andreas Seeger

We prove a sharp boundedness result on $L^{4} (R^{2})$ for mollifications of the disc multiplier.

math.CA2026

A lower bound for a variation norm operator associated with circular means

David Beltran, Anthony Carbery, Luz Roncal +1

We prove that a local $L^{p} (V_{2})$ variation norm estimate fails for circular means in two dimensions, and quantify this failure by proving lower bounds for functions of exponential…

math.CA2026

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 $L^{p} (∣ x ∣^{α})$ spaces. Aside from endpoint cases, a complete description of…

math.CA2025

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.

math.CA2025

A fractal local smoothing problem for the wave equation

David Beltran, Joris Roos, Alex Rutar +1

For any given set $E \subset [1, 2]$ , we discuss a fractal frequency-localized version of the $L^{p}$ local smoothing estimates for the half-wave propagator with times in $E$ . A conjec…

math.CA2024

Spherical maximal operators with fractal sets of dilations on radial functions

David Beltran, Joris Roos, Andreas Seeger

For a given set of dilations $E \subset [1, 2]$ , Lebesgue space mapping properties of the spherical maximal operator with dilations restricted to $E$ are studied when acting on radia…