From the 1 of 5 linked papers with an AI index.
5 papers
Power weight inequalities for spherical maximal functions
Marco Fraccaroli, Joris Roos, Andreas Seeger
The paper characterizes the range of exponents for which spherical maximal operators with general dilation sets are bounded on weighted L^p spaces with power weights |x|^α, using t…
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.
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…
A lower bound for a variation norm operator associated with circular means
David Beltran, Anthony Carbery, Luz Roncal +1
We prove that a local variation norm estimate fails for circular means in two dimensions, and quantify this failure by proving lower bounds for functions of exponential…
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…