5 papers · 1 filter
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…
Endpoint estimates for the fractal circular maximal function and related local smoothing
Sanghyuk Lee, Luz Roncal, Feng Zhang +1
Sharp -- estimates for the spherical maximal function over dilation sets of fractal dimensions, including the endpoint estimates, were recently proved by Anderson--Hughes…
Weighted Weak Type estimates for non-integral Square Functions
Dario Mena, Maria Carmen Reguera, Luz Roncal
We provide quantitative weighted weak type estimates for non-integral square functions in the critical case in terms of the and reverse Hölder constants associated to t…
On differentiation of integrals in Lebesgue spaces
Marco Fraccaroli, Dariusz Kosz, Luz Roncal
We study the problem of differentiation of integrals for certain bases in the infinite-dimensional torus . In particular, for every , we construct…
On the absolute divergence of Fourier series in the infinite dimensional torus
E. Fernández, L. Roncal
We present some simple counterexamples, based on quadratic forms in infinitely many variables, showing that the implication $f\in C^{(\infty}(\mathbb{T}^ω)\Longrightarrow\sum_{\bar…