司靈得 (Daniel Spector)

Fall 2026 Nonlinear Analysis Seminar Series

Past Seminars
*This section archives the event information, speakers, and abstracts of our past seminars (Fall 2026 onward).
*Looking for lecture recordings? Seminar recordings prior to Fall 2026 are hosted in the Video Library section of this website.

Date: Tuesday, 22 Sep. 2026, 15:00-16:00 TST (GMT+8) , in Room M212 in NTNU Gongguan Campus Mathematics Building
Speaker: Chun Ho Lau, National Taiwan Normal University
Title: When (does) a singular integral operator maps atoms to molecules
Abstract:
In real Hardy spaces $H^p(\mathbb{R}^n)$ for $0 < p \le 1$, to check whether a singular integral operator $T$ is bounded on $H^p(\mathbb{R}^n)$, it is common to show that $T(a)$ is a molecule with the assumption that $T^*(1) = 0$. In this talk, we consider a similar situation in the local Hardy spaces $h^p(\mathbb{R}^n)$, with a broader class of molecules defined by a weaker cancellation condition. Moreover, we will discuss the properties of the singular integral operator if it maps atoms to molecules. This talk is based on the papers with Galia Dafni, Tiago Picon, and Claudio Vasconcelos.

Date: Tuesday, 29 Sep. 2026, 15:00-16:00 TST (GMT+8), in Room M212 in NTNU Gongguan Campus Mathematics Building
Speaker: Guy Foghem, Brandenburg University of Technology Cottbus-Senftenberg
Title: Robust interpolation inequalities via Chebyshev-type integral inequalities
Abstract:
We establish robust log-convex interpolation inequalities within the scale of Gagliardo seminorms. We achieve this by deriving some Chebyshev-type integral inequalities for general non-synchronous functions. An application for establishing these robust interpolation inequalities stems from the study of the asymptotic nonlocal-to-local optimal stability of weak solutions to the boundary Dirichlet problem associated with the regional fractional $p$-Laplacian. More precisely, if $u_s \in W^{s,p}(\Omega)$ weakly satisfies $(-\Delta)_{p,\Omega}^s u_s = f_s$ in $\Omega$ and $\gamma_0^s(u_s) = g_s$ on $\partial\Omega$, with $\frac{1}{p} < s \le 1$ and $\Omega \subset \mathbb{R}^d$ is bounded Lipschitz, then, under appropriate convergence of the data $f_s$ and $g_s$ as $s \to 1^-$, we establish that $\|u_s - u_1\|_{W^{s,p}(\Omega)} \xrightarrow{s \to 1^-} 0$.