论文标题
Carleson嵌入Tri-Tree和Tri-Disc上
Carleson embedding on tri-tree and on tri-disc
论文作者
论文摘要
我们证明多参数二元嵌入了多树上的Hardy操作员定理。我们还表明，对于Bi-Disc和Tri-Disc中的大量Dirichlet空间，这证明了荷兰式功能在Bi-和Tri-Disc上的Dirichlet空间的嵌入定理。我们完全描述了此类嵌入的Carleson措施。下面的结果概括了\ cite {ampvz}的嵌入结果，从双树到三树。我们的嵌入描述之一类似于Carleson-chang-fefferman条件，涉及二元开放式。另一方面，\ cite {ampvz}的异常特征是嵌入双树上的特征与一个盒子的情况相等。这与Chang-Fefferman和众所周知的Carleson被子反例的作品显着差异。我们在这里证明了Tri-Tree的出乎意料的结果。最后，我们解释了阻止我们在四个及更高尺寸的多盘上证明我们的结果的障碍。
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 that embedding on bi-tree turned out to be equivalent to one box Carleson condition. This is in striking difference to works of Chang--Fefferman and well known Carleson quilt counterexample. We prove here the same unexpected result for the tri-tree. Finally, we explain the obstacle that prevents us from proving our results on polydiscs of dimension four and higher.
