论文标题
在不同尺寸的空间上的热内核估计值
Heat kernel estimates on spaces with varying dimension
论文作者
论文摘要
我们在尺寸不同的空间上获得了尖锐的两侧热内核估计，其中一个点连接了两个通用尺寸的空间。在这些空间上，如果两个构成部分的尺寸不同，则相对于相关的Lebesgue度量引起的度量，体积倍增的属性失败。因此，抛物线抛物线不平等现象失败，热核不享受Aronson型估计。我们的估计表明，对基因的估计值独立于少量空间的两个部分的尺寸，而它们依赖于它们的瞬时或重复发生。这些是Z.-Q.考虑的空间的多维版本。 Chen和S. Lou（Ann。prob。2019），其中一点点空间和一个二维空间在一个点连接。
We obtain sharp two-sided heat kernel estimates on spaces with varying dimension, in which two spaces of general dimension are connected at one point. On these spaces, if the dimensions of the two constituent parts are different, the volume doubling property fails with respect to the measure induced by the associated Lebesgue measures. Thus the parabolic Harnack inequalities fail and the heat kernels do not enjoy Aronson type estimates. Our estimates show that the on-diagonal estimates are independent of the dimensions of the two parts of the space for small time, whereas they depend on their transience or recurrence for large time. These are multidimensional version of a space considered by Z.-Q. Chen and S. Lou (Ann. Probab. 2019), in which a 1-dimensional space and a 2-dimensional space are connected at one point.
