On singular monotonic functions whose spectrum has a given Hausdorff dimension
On singular monotonic functions whose spectrum has a given Hausdorff dimension
复制标题
关于谱具有给定豪斯多夫维数的奇异单调函数
DOI：
--
复制
发表时间：
1951
期刊：
影响因子：
--
通讯作者：
R. Salem
中科院分区：
文献类型：
--
作者：
R. Salem
1）。定理I可以从定理II推导出来，但由于证明的方法是相同的，所以我们证明了这两个定理。2）。定理I已在较早的一篇论文中证明，对于r = 1的情况（集合的勒贝格测度当然为零），甚至在更强的形式下，奇异函数的傅里叶-斯蒂尔捷斯变换对每个q > 2都是Lq。论证与本文件相同，但要简单得多。我们接下来证明：
1). Theorem I could be deduced from Theorem II, but since the method of the proof is the salne, we prove both theorems. 2). Theorem I has been proved in an earlier paper* for the case r = 1 (the Lebesgue measure of the set being of course zero), even in the stronger form, that the Fourier Stieltjes transform of the singular function beh)ngs to L q for every q > 2. The argument is the same as in the present paper, although much simpler. We next prove: