Liang-Chuan Wu

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20242026

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4 papers · 1 filter

math.AP2024

Hölder regularity and Liouville Theorem for the Schrödinger equation with certain critical potentials, and applications to Dirichlet problems

Bo Li, Ji Li, Liangchuan Wu

Let $(X, d, μ)$ be a metric measure space satisfying a doubling property with the upper/lower dimension $Q \geq n > 1$ , and admitting an $L^{2}$ -Poincaré inequality. In this article, we es…

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.AP2024

Global-in-time maximal regularity for the Cauchy problem of the heat equation in BMO and applications

Xuan Thinh Duong, Ji Li, Liangchuan Wu +1

In this article, we establish global-in-time maximal regularity for the Cauchy problem of the classical heat equation $\partial_{t} u (x, t) - Δ u (x, t) = f (x, t)$ with $u (x, 0) = 0$ in a certai…

math.CA2024

Schatten classes and commutators in the two weight setting, II. Riesz transforms

Michael Lacey, Ji Li, Brett D. Wick +1

We characterize the Schatten class $S^{p}$ of the commutator of Riesz transforms $[b, R_{j}]$ in $R^{n}$ ( $j = 1, \dots, n$ ) in the two weight setting for $n < p < \infty$ , by introduc…