Peng Chen

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math.CA2024

On maximal functions generated by Hörmander-type spectral multipliers

Peng Chen, Xixi Lin, Liangchuan Wu +1

Let $(X, d, μ)$ be a metric space with doubling measure and $L$ be a nonnegative self-adjoint operator on $L^{2} (X)$ whose heat kernel satisfies the Gaussian upper bound. We assume tha…

math.CA2024

On pointwise convergence of cone multipliers

Peng Chen, Danqing He, Xiaochun Li +1

For $p \geq 2$ , and $λ > max {n ∣ \frac{1}{p} - \frac{1}{2} ∣ - \frac{1}{2}, 0}$ , we prove the pointwise convergence of cone multipliers, i.e. $t \to \infty lim T_{t}^{λ} (f) \to f a.e.,$ whe…

math.CA2023

A weighted L^2 estimate of Commutators of Bochner-Riesz Operators for Hermite operator

Peng Chen, Xixi Lin

Let H be the Hermite operator -Δ+|x|^2 on \mathbb{R}^n. We prove a weighted L^2 estimate of the maximal commutator operator \sup_{R>0}|[b, S_R^λ(H)](f)|, where [b, S_R^λ(H)](f) = b…