与Walsh-Paley系统相关的张量积算子序列的极限
Limits of sequence of Tensor Product Operators associated with the Walsh-Paley system
AI总结：
本文针对两个加权一维Walsh-Fourier级数张量积的极大算子，利用一维算子的一致有界性建立弱型不等式，并证明在二维Walsh-Lebesgue点上的收敛性。
摘要：
众所周知，要建立$L_1$空间上算子序列的几乎处处收敛性，只需获得该算子序列对应的极大算子的弱$(1,1)$型不等式即可。然而，在实际应用中，为极大算子建立上述不等式是一项非常棘手且困难的工作。本文的主要目标是对两个加权一维Walsh-Fourier级数的张量积所对应的上述不等式提出一种新的视角。具体而言，我们的主要思路是自然地考虑序列的一致有界性条件，这些条件蕴含张量积的极大算子的弱型估计。更精确地说，我们将在相应的一维算子具有一致有界性的前提下，建立二维极大算子的张量积的弱型不等式。此外，在二维Walsh-Lebesgue点上，还建立了算子张量积的收敛性。
英文摘要：
It is well-known that to establish the almost everywhere convergence of a sequence of operators on $L_1$-space, it is sufficient to obtain a weak $(1,1)$-type inequality for the maximal operator corresponding to the sequence of operators. However, in practical applications, the establishment of the mentioned inequality for the maximal operators is very tricky and difficult job. In the present paper, the main aim is a novel outlook at above mentioned inequality for the tensor product of two weighted one-dimensional Walsh-Fourier series. Namely, our main idea is naturally to consider uniformly boundedness conditions for the sequences which imply the weak type estimation for the maximal operator of the tensor product. More precisely, we are going to establish weak type of inequality for the tensor product of two dimensional maximal operators while having the uniform boundedness of the corresponding one dimensional operators. Moreover, the convergence of the tensor product of operators is established at the two dimensional Walsh-Lebesgue points.
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。
