Sharp estimates of the Jacobi heat kernel

Sharp estimates of the Jacobi heat kernel
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雅可比热核的精确估计

DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
P. Sjogren
P. Sjogren
中科院分区：
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文献类型：
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作者：
A. Nowak;P. Sjogren

文献摘要

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与经典雅可比多项式的设定相关的热核是由一个振荡和定义的，该和不能被显式计算，这与另外两个经典的正交多项式系统的情况相反。对于类型参数$α，ETA ge-1/2$，我们给出了给出这个核的量级的精确估计。作为上界的应用，我们证明了多维Jacobi热半群的极大算子满足弱型$(1，1)$不等式。我们还得到了Poisson-Jacobi核的精确估计。
The heat kernel associated with the setting of the classical Jacobi polynomials is defined by an oscillatory sum which cannot be computed explicitly, in contrast to the situation for the two other classical systems of orthogonal polynomials. We deduce sharp estimates giving the order of magnitude of this kernel, for type parameters $alpha,eta ge -1/2$. As an application of the upper bound obtained, we show that the maximal operator of the multi-dimensional Jacobi heat semigroup satisfies a weak type $(1,1)$ inequality. We also obtain sharp estimates of the Poisson-Jacobi kernel.