4 papers · 1 filter
Asymptotically sharp embedding of into for flat weights and applications to Poincaré-Sobolev inequalities
Alejandro Claros, Ezequiel Rela
We provide new quantitative results on the embedding of the Muckenhoupt class into with the correct asymptotic behavior when the Fujii--Wilson constant $[w]_{A_\in…
Slowly decaying Rajchman measures and a restriction theorem for the Fourier transform at the limit case of zero Fourier dimension
Iván Polasek, Ezequiel Rela
In this article we prove the existence of sets of zero Fourier dimension such that it is possible to restrict the Fourier transform to on a certain non…
Weighted Sobolev Inequalities via the Meyers--Ziemer Framework: Measures, Isoperimetric Inequalities, and Endpoint Estimates
Simon Bortz, Kabe Moen, Andrea Olivo +2
We establish a new global endpoint Sobolev inequality for measures that extends the classical theorem of Meyers-Ziemer by placing a maximal function on the right-hand side. This re…
The exact dimension of Liouville numbers: The Fourier side
Iván Polasek, Ezequiel Rela
In this article we study the generalized Fourier dimension of the set of Liouville numbers . Being a set of zero Hausdorff dimension, the analysis has to be done at the…