8 papers
Coarea Reduction, Sparse Transfer, and Geometric Recomposition for Synchronized Singular Forms
Vicente Vergara
We study truncated bilinear forms associated with synchronized kernels \[ K(x,y)=k(Ï(x),Ï(y)), \] where the singularity is governed by a one-dimensional kernel , while the geo…
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…
Dyadic microlocal partitions for position-dependent fiber metrics and Weyl quantization
Vicente Vergara
We construct a dyadic microlocal partition adapted to a position-dependent fiber metric on phase space and quantify its interaction with Weyl quantization. Under uniform ellipticit…
An optimal trace estimate for microlocal square functions on quadratic surfaces
Vicente Vergara
We study a local trace estimate for the microlocal angular square function \[ G_R f := \left(\sum_Î|f_Î|^2\right)^{1/2} \] associated with a parabolic decomposition of the freque…
-variational capacity of interior condensers and geometric reduction by a fixed phase
Vicente Vergara
We study the -variational capacity of interior condensers in a bounded open set when both plates are determined by a single phase in $…
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 Gabor frames with q…