Bernstein inequality for multivariate functions with smooth Fourier images

• Date: 2026
• Main Authors: Bang, Ha Huy, Huy, Vu Nhat
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2026
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/6386
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 Let $K$ be a compact set in ${\Bbb R}^n$ with $(O)$-property and let $1\leq p\leq \infty$. Then there exists a constant $C_K< \infty $ independent of $f$ and $\alpha$ such that $$\|D^{\alpha } f \|_p \leq C_K \sup\limits_{\xi \in K } |\xi ^{\alpha} |\, \|f\|_{\mathcal{H}_{p,K,3}...