对称锥上管域中的Duren-Carleson定理
The Duren-Carleson theorem in tube domains over symmetric cones
摘要：
在对称锥上的管域$T_Ω$中，研究了Hardy空间$H^p$连续嵌入Lebesgue空间$L^q (T_Ω, dμ)$中的正Borel测度$μ$的特征，$0<p<q<\infty.$推广了Blasco关于单位圆盘的结果，将问题化为标准测度.我们得到了Hardy空间$H^{p}$，$1\leq p < \infty,$连续嵌入指数较大的加权Bergman空间.最后利用这个结果对每个正整数$m$刻画了从$H^{2m}$到Bergman空间的乘子.
英文摘要：
In the setting of tube domains over symmetric cones, $T_Ω$, we study the characterization of the positive Borel measures $μ$ for which the Hardy space $H^p$ is continuously embedded into the Lebesgue space $L^q (T_Ω, dμ)$, $0<p<q<\infty.$ Extending a result due to Blasco for the unit disc, we reduce the problem to standard measures. We obtain that a Hardy space $H^{p}$, $1\leq p < \infty,$ embeds continuously in weighted Bergman spaces with larger exponents. Finally we use this result to characterize multipliers from $H^{2m}$ to Bergman spaces for every positive integer $m$.
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。
