Michel Alexis

activity

20142023

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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

Haar basis testing

The scalar T1 theorem for pairs of doubling measures fails for Riesz transforms when p not 2

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

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