论文标题
Menchov-Rademacher操作员的右三角形的上限
An Upper Bound for the Menchov-Rademacher Operator for Right Triangles
论文作者
论文摘要
Menchov-Rademacher不平等是谐波分析中的不平等，范围限制了某个最大操作员的$ L_2 $规范。它首先是为了证明一系列正交函数的几乎到处的融合。当考虑两参数序列的正交函数时，将该系列的确切方式分组就变得必不可少。我们将考虑将一个两参数系列的分组，该系列由一系列右三角形产生，在原点上有一个顶点，后者可能是非平衡的，并且当这些三角形的偏心率有界限时，几乎可以在任何地方融合。为了执行证据，我们将获得Menchov-Rademacher不平等的类似物，以备右三角形。
The Menchov-Rademacher inequality is an inequality in harmonic analysis that bounds the $L_2$ norm of a certain maximal operator. It was first established in order to prove almost everywhere convergence of a one-parameter series of orthogonal functions. When two-parameter series of orthogonal functions is considered, the exact way the series is grouped becomes essential. We will consider grouping of a two-parameter series, generated by a sequence of right triangles with a vertex at the origin, who might be non-equilateral, and prove almost everywhere convergence when the eccentricity of those triangles is bounded. In order to carry out the proof, we will derive an analogue of the Menchov-Rademacher inequality for right triangles.
