论文标题
扩展和跟踪非划分双倍空间的定理
Extension and trace theorems for noncompact doubling spaces
论文作者
论文摘要
我们将Björn-Björn-Shanmugalingam \ cite {bbs21}的扩展和痕量结果推广到完整的非稳定度量度量空间及其均匀的双曲线填充物的设置。这是通过作者提出的统一过程来完成的，该过程使用Busemann函数统一均匀的双曲线空间，而不是Bonk-Heinonen-Koskela \ cite {bhk}的工作中考虑的距离函数。我们为BESOV空间推定了几种定义的定义，这些定义是以这种方式作为痕迹空间出现的，包括存在与BESOV容量相对于BESOV的能力，存在$ l^p $ - lebesievery的存在与BESOV容量相对于hölder的态度越来越多的努力和强度的努力，并提出了较高的努力，并提出了较高的努力。我们还获得了几种庞加莱型的不等式，将球上的BESOV功能的积分与这些功能扩展的上梯度的积分与空间的均匀双曲线填充的积分相关。
We generalize the extension and trace results of Björn-Björn-Shanmugalingam \cite{BBS21} to the setting of complete noncompact doubling metric measure spaces and their uniformized hyperbolic fillings. This is done through a uniformization procedure introduced by the author that uniformizes a Gromov hyperbolic space using a Busemann function instead of the distance functions considered in the work of Bonk-Heinonen-Koskela \cite{BHK}. We deduce several corollaries for the Besov spaces that arise as trace spaces in this fashion, including the existence of representatives that are quasicontinuous with respect to the Besov capacity, the existence of $L^p$-Lebesgue points quasieverywhere with respect to the Besov capacity, embeddings into Hölder spaces for appropriate exponents, and a stronger Lebesgue point result under an additional reverse doubling hypothesis on the measure. We also obtain several Poincaré-type inequalities relating integrals of Besov functions over balls to integrals of upper gradients of extension of these functions to a uniformized hyperbolic filling of the space.
