论文标题
在Martingale Hardy空间上的有限操作员
Bounded operators on Martingale Hardy spaces
论文作者
论文摘要
我论文的目的是讨论，发展和应用与现代谐波分析有关的迷人理论的最新发展。特别是，我们研究了Vilenkin-Fourier系列的部分总和的某些强大收敛性结果。此外，我们为连续性模量提供了必要和充分的条件，因此Fejér均值的规范收敛是有效的。此外，我们考虑了Riesz和Nörlund对数手段。还证明，从特殊意义上讲，这些结果是最好的。指出了某些知名和新结果的应用。此外，我们研究了一些$ t $均值，这些均值是nörlund的“反相反”方法，但仅在其系数为单调的情况下。
The aim of my thesis is to discuss, develop and apply the newest developments of this fascinating theory connected to modern harmonic analysis. In particular, we investigate some strong convergence result of partial sums of Vilenkin-Fourier series. Moreover, we derive necessary and sufficient conditions for the modulus of continuity so that norm convergence of subsequences of Fejér means is valid. Furthermore, we consider Riesz and Nörlund logarithmic means. It is also proved that these results are the best possible in a special sense. As applications both some well-known and new results are pointed out. In addition, we investigate some $T$ means, which are "inverse" summability methods of Nörlund, but only in the case when their coefficients are monotone.
