J. L. Luna-Garcia

activity

20212023

collaborators

7 papers

math.FA2023

Haar basis testing

Michel Alexis, Jose Luis Luna-Garcia, Eric T. Sawyer

We show that for two doubling measures $σ$ and $ω$ on $R^{n}$ and any fixed dyadic grid $D$ in $R^{n}$ , \[ \mathfrak{N}_{\mathbf{R}^{λ, n}}\left( σ,ω\ri…

math.CA2023

The scalar $T 1$ theorem for pairs of doubling measures fails for Riesz transforms when p not 2

Michel Alexis, José Luis Luna-Garcia, Eric Sawyer +1

We show that for an individual Riesz transform in the setting of doubling measures, the scalar $T 1$ theorem fails when $p \neq = 2$ : for each $p \in (1, \infty) ∖ {2}$ , we…

math.FA2023

The T1 theorem for the Hilbert transform fails when p is not 2

Michel Alexis, Jose Luis Luna-Garcia, Eric T. Sawyer +1

Given p between 1 and infinity, but not 2, we show that the T1 theorem for the Hilbert transform fails for L^{p}, despite holding for p equal to 2

math.CA2022

Stability of Weighted Norm Inequalities

Michel Alexis, José Luis Luna Garcia, Eric Sawyer +1

We show that while individual Riesz transforms are two weight norm stable under biLipschitz change of variables on $A_{\infty}$ weights, they are two weight norm unstable under eve…

math.CA2021

Parabolic Singular Integrals with Nonhomogeneous Kernels

Simon Bortz, John Hoffman, Steve Hofmann +2

We establish $L^{2}$ boundedness of all "nice" parabolic singular integrals on "Good Parabolic Graphs", aka {\em regular} Lip(1,1/2) graphs. The novelty here is that we include non-h…

math.MG2021

Corona Decompositions for Parabolic Uniformly Rectifiable Sets