Author

Ahmed Dughayshim

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Preprint Sep 2026

The Trudinger inequality is true for $M^{1,s}$ spaces

We prove the Trudinger inequality with exponent $\frac{s}{s-1}$ for $M^{1,s}$ Sobolev spaces on metric measure spaces under the sole measure growth assumption $\mu(B(x,r))\ge br^s$. This improves the previously known exponential integrability with power one. Our argument also yields sharp asymptotic bounds for the Sobo...

R. Alvarado, Ahmed Dughayshim, P. Hajłasz · 0 citations

Preprint Oct 2026

Global existence of the $s$-Schr\"odinger maps in $n \geq 5$

We study the $s$-Schr\"odinger map equation \[ \begin{cases} \partial_t u = -u \wedge (-\Delta)^s u \quad \text{on } \mathbb{R}^n \times \mathbb{R}\\ u: \mathbb{R}^n \times \mathbb{R} \to \mathbb{S}^2\\ u(x,0) = u_0. \end{cases} \] For $s \in (1/2,1)$ and $n \geq 5$ we prove that for small initial data $u_0$ in the cri...

Ahmed Dughayshim, Armin Schikorra · 0 citations