$L^p$ -可积性、傅里叶变换支集的维数及其应用
$L^p$-integrability, dimensions of supports of fourier transforms and applications
摘要：
本文证明了具有$1\leq p\leq 2n/α$的$L^p(\R^n)$中不存在任何非零函数，只要它的傅里叶变换由一组有限填充$α$ -测度支持，其中$0<α<n$ .结果表明，断言失败的$p>2n/α$。应用该结果证明了关于$\R^n$和M（2）的$L^p$ Wiener-Tauberian定理.
英文摘要：
It is proved that there does not exist any non zero function in $L^p(\R^n)$ with $1\leq p\leq 2n/α$ if its Fourier transform is supported by a set of finite packing $α$-measure where $0<α<n$. It is shown that the assertion fails for $p>2n/α$. The result is applied to prove $L^p$ Wiener-Tauberian theorems for $\R^n$ and M(2).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
