论文标题
非椭圆形schrödinger平均序列的急剧收敛性
Sharp convergence for sequences of nonelliptic Schrödinger means
论文作者
论文摘要
我们考虑非ellipticschrödinger的点融合表示$ e^{it_ {n} \ square} f（x）$ for $ f \ in H^{s}（\ Mathbb {r}^{2} {2}）$ in零，其中\ [{ }}}}}}}}} \ wideHat {f}} \ left（ξ\ right）dξ。\]我们证明，当$ 0 <s <s <s <\ frac {1} {2} {2} {2} $，\ \ \ \ [\ mathop {\ lim} {\ lim} \ limits_ { }} f \ left（x \ right）= f（x）\ hspace {0.2cm} a.e。\ hspace {0.2cm} x \ in \ mathbb {r}^2 \]保留所有$ f \ in { $ \ {t_ {n} \} _ {n = 1}^{\ infty} \ in \ ell^{r（s），\ infty}（\ mathbb {n}）$，$ r（s）= \ frac {s} {1-s} {1-s} {1-s} $。此外，我们的结果在一般维度上仍然有效。
We consider pointwise convergence of nonelliptic Schrödinger means $e^{it_{n}\square}f(x)$ for $f \in H^{s}(\mathbb{R}^{2})$ and decreasing sequences $\{t_{n}\}_{n=1}^{\infty}$ converging to zero, where \[{e^{it_{n}\square }}f\left( x \right): = \int_{{\mathbb{R}^2}} {{e^{i\left( {x \cdot ξ+ t_{n}{{ ξ_{1}ξ_{2} }}} \right)}}\widehat{f}} \left( ξ\right)dξ.\] We prove that when $0<s < \frac{1}{2}$, \[\mathop {\lim }\limits_{n \to \infty} {e^{it_{n}\square }}f\left( x \right) = f(x) \hspace{0.2cm} a.e.\hspace{0.2cm} x\in \mathbb{R}^2\] holds for all $f \in {H^s}\left( {{\mathbb{R}^2}} \right)$ if and only if $\{t_{n}\}_{n=1}^{\infty} \in \ell^{r(s), \infty}(\mathbb{N})$, $r(s)=\frac{s}{1-s}$. Moreover, our result remains valid in general dimensions.
