关于Walsh-傅里叶级数的Nörlund对数平均连续性的一些新结果
Some new results for subsequences of Nörlund logarithmic means of Walsh-Fourier series
摘要：
证明了存在一个鞅$f\in H_p $，使得对于$0<p<1 $，Nörlund对数平均的子序列$\{L_{2^n}f \}$在Lebesgue空间$weak-L_p $中是有界的.证明了对任意$f\in L_p(G),$ $p\geq 1, $，$L_{2^n}f$在任意Lebesgue点$x$收敛于$f$.导出了一些新的相关不等式。
英文摘要：
We prove that there exists a martingale $f\in H_p $ such that the subsequence $\{L_{2^n}f \}$ of Nörlund logarithmic means with respect to the Walsh system are not bounded in the Lebesgue space $weak-L_p $ for $0<p<1 $. Moreover, we prove that for any $f\in L_p(G),$ $p\geq 1, $ $L_{2^n}f$ converge to $f$ at any Lebesgue point $x$. Some new related inequalities are derived.
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。
