5 papers · 1 filter
Strong-type endpoint obstructions for bilinear spherical maximal operators
Vicente Vergara
For the bilinear spherical averages in dimension , we show that the lacunary maximal operator is not bounded from to $L^r(\mathbb…
Normal-Direction Energy and Fourier Restriction for Convex Planar Curves
Vicente Vergara
We study Fourier extension from compact convex planar curves by organizing the mass through the Gauss map. The pushforward measure \[ ν_f= N_\#\bigl(|f|^2…
Logarithmic oscillatory multipliers and log-subdyadic square functions
Vicente Vergara
We develop square-function estimates for Fourier multipliers whose local oscillation scale is \[ ρ(R)=\frac{R}{(\log R)^{γ-1}}, \qquad γ>1. \] This scale lies strictly between the…
Coarea Reduction, Sparse Transfer, and Geometric Recomposition for Synchronized Singular Forms
Vicente Vergara
We study truncated bilinear forms associated with synchronized kernels \[ K(x,y)=k(ϕ(x),ψ(y)), \] where the singularity is governed by a one-dimensional kernel , while the geome…
Subdyadic time-frequency analysis: Gabor frames, modulation spaces, and Miyachi multipliers
Vicente Vergara
We present a time-frequency framework adapted to dispersive phase functions via a subdyadic geometry in phase space. On top of this geometry we construct stable frequency-adaptive…