论文标题
抛物线的抛物线在同质类型的空间上
Parabolic Muckenhoupt Weights on Spaces of Homogeneous Type
论文作者
论文摘要
这项工作讨论了同质类型的空间上的抛物线粉碎，即具有倍增度量和附加单调的大地测量特性的\ quasi-metric空间。主要结果包括对抛物线最大操作员加权规范不等式的表征，反向Hölder不平等以及此类权重的琼斯型分解结果。通过施加抛物线寄生虫John-Nirenberg引理，研究了抛物线有限平均振荡和抛物线粉碎权重之间的连接。还给出了抛物线界面平均振荡空间的Coifman-抛物线最大函数方面的表征。抛物线理论中的主要挑战与估计值的时间滞后有关。结果是由相应的欧几里得理论和公制度量空间上的抛物线变异问题的规律性理论激励的。
This work discusses parabolic Muckenhoupt weights on spaces of homogeneous type, i.e.\ quasi-metric spaces with both a doubling measure and an additional monotone geodesic property. The main results include a characterization in terms of weighted norm inequalities for parabolic maximal operators, a reverse Hölder inequality, and a Jones-type factorization result for this class of weights. The connection between the space of parabolic bounded mean oscillation and parabolic Muckenhoupt weights is studied by applying a parabolic John--Nirenberg lemma. A Coifman--Rochberg-type characterization of the space of parabolic bounded mean oscillation in terms of parabolic maximal functions is also given. The main challenges in the parabolic theory are related to the time lag in the estimates. The results are motivated by the corresponding Euclidean theory and the regularity theory for parabolic variational problems on metric measure spaces.
