上半平面Hardy-Orlicz空间的分解与原子分解及其在Hankel算子中的应用
Factorization and Atomic Decomposition in Hardy-Orlicz Spaces on the Upper Half-Plane with Applications to Hankel Operators
AI总结：
该研究建立上半平面Hardy-Orlicz空间的强分解与原子分解，将其应用于分析Hankel算子的连续性，完善了此类函数空间的理论框架。
AI中文摘要：
本研究建立了上半平面Hardy-Orlicz空间的强分解定理，证明分别属于Hardy-Orlicz空间$H^{\Phi_{1}}$和$H^{\Phi_{2}}$的两个函数的乘积属于第三个空间$H^{\Phi_{3}}$，且$H^{\Phi_{3}}$中的每个全纯函数都可进行此类分解。随后，针对特定Hardy-Orlicz空间给出原子分解，该分解可在关联函数为凹函数时描述这些空间的拓扑对偶。最后，将上述结果应用于研究该框架下Hankel算子的连续性。
英文摘要：
In this work, we establish a strong factorization for Hardy-Orlicz spaces on the upper half-plane. We show that the product of two functions belonging respectively to Hardy-Orlicz spaces $H^{Φ_{1}}$ and $H^{Φ_{2}}$ lies in a third space $H^{Φ_{3}}$, and every holomorphic function in $H^{Φ_{3}}$ admits such a decomposition. We then provide an atomic decomposition for certain Hardy-Orlicz spaces, which allows us to describe the topological dual of these spaces when the associated function is concave. Finally, these results are applied to the study of the continuity of the Hankel operators in this setting.
