The Bellman function of the dyadic maximal operator in connection with the Dyadic Carleson Imbedding Theorem

Properties of the Bellman function related to the Carleson Imbedding theorem for the dyadic maximal operator

We provide a description for the Bellman function related to the Carleson Imbedding theorem, first mentioned in [4], with the use of the Hardy operator.

与孔隙集相关的Carleson立方体族

Carleson families of cubes related to porous sets

本文研究了孔隙集与dyadic覆盖之间的反问题，改进了Carleson打包条件和稀疏性性质，探讨了生成孔隙集的Carleson族特性。

Haar型与Carleson常数

Haar Type and Carleson Constants

我们确定子集合的并元区间，能够检测Haar型的巴拿赫空间。基本的二分法表示的Carleson包装条件。

算子值并元BMO空间

Operator-valued dyadic BMO spaces

我们考虑算子值函数的BMO空间，其中算子值函数空间$B$定义了$L^2(H)$上的有界仿积。本文利用$B$的“扫掠”函数的范数或$B$的鞅变换的范数的平均，得到了$\|π_B\|$的几个等价形式.此外，我们通过一个仿积的乘积公式研究了John-Nirenberg型不等式与Carleson型不等式之间的联系，并给出了John-Nirenberg型不等式的精确维数估计.

Carleson embedding on tri-tree and on tri-disc

We prove multi-parameter dyadic embedding theorem for Hardy operator on the multi-tree. We also show that for a large class of Dirichlet spaces in bi-disc and tri-disc this proves the embedding theorem of those Dirichlet spaces of holomorphic function on bi- and tri-disc. We completely describe the Carleson measures for such embeddings. The result below generalizes embedding result of \cite{AMPVZ} from bi-tree to tri-tree. One of our embedding description is similar to Carleson--Chang--Fefferman condition and involves dyadic open sets. On the other hand, the unusual feature of \cite{AMPVZ} was…

L_p并矢鞅的有界变差逼近与椭圆型方程的解

Bounded variation approximation of L_p dyadic martingales and solutions to elliptic equations

我们证明了连续性和满射的迹映上$L_p$，从一个空间的功能的局部有界的变化，定义的Carleson功能。扩展映射是通过一个停时参数构造的。这扩展了Varopoulos在BMO情况下与Corona定理相关的早期工作。我们还证明了椭圆型非光滑散度型方程解的$L_p$ Carleson逼近性结果，推广了Hofmann，Kenig，Mayboroda和Pipher在$p=\infty$情形下的结果.