Peng Chen

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math.CA2024

On maximal functions generated by HÃ¶rmander-type spectral multipliers

Peng Chen, Xixi Lin, Liangchuan Wu +1

Let $(X, d, I^¼)$ 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 th…

math.CA2024

On pointwise convergence of cone multipliers

Peng Chen, Danqing He, Xiaochun Li +1

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