11 papers
Weighted Fourier capacities and Frostman restriction estimates
Rodrigo Leon, Vicente Vergara
We study a weighted Fourier capacity attached to compact sets, $ c_{p,k}(K)=\inf\left\{\|k\widehat u\|_{L^p(\mathbb{R}^d)}:u\in C_0^\infty(\mathbb{R}^d),\ u\geq 1 \text{ on } K\rig…
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…
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 \[ G_R f := \left(\sum_Θ|f_Θ|^2\right)^{1/2} \] associated with a parabolic decomposition of the frequenc…
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…
-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 $W^{…
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…
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…
A non-Gaussian Hardy-type Equation in Fractional Time
Soveny Solís, Vicente Vergara
A non-Gaussian Hardy equation is studied with a non-linearity of Osgood-type growth. A fractional derivative in time is incorporated for the first time in an research of this type.…
Non-existence of solutions for a non-Gaussian equation in fractional time with Osgood type nonlinearity
Soveny Solís, Vicente Vergara
Osgood functions in the source term are used to produce results for non-existence of local solutions into the framework of non-Gaussian diffusion equations. The critical exponent f…