The high-dimensional version of Fatou’s classical theorem asserts that the Poisson semigroup of a function $$f\in L_{p}(\mathbb {R}^{n}), \ 1\le p \le \infty $$, converges to f non-tangentially at Lebesque points. In this paper we investigate the rate of non-tangential convergence of Poisson and metaharmonic semigroups at $$\mu $$-smoothness points of f.

中文翻译：

---

关于泊松半群和修正泊松半群在 $$L_{p}$$Lp 函数平滑点处的非切向收敛

Fatou 经典定理的高维版本断言函数 $$f\in L_{p}(\mathbb {R}^{n}), \ 1\le p \le \infty $$ 的泊松半群，在 Lebesque 点非切向收敛到 f。在本文中，我们研究了泊松和元谐波半群在 f 的 $$\mu $$-平滑点处的非切向收敛率。