Generalized Fractional Integral Operators Based on Symmetric Markovian Semigroups with Application to the Heisenberg Group
Generalized Fractional Integral Operators Based on Symmetric Markovian Semigroups with Application to the Heisenberg Group
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DOI：
10.11650/tjm/220904
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发表时间：
2022-01
影响因子：
0.4
通讯作者：
Kohei Amagai;E. Nakai;Gaku Sadasue
中科院分区：
文献类型：
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作者：
Kohei Amagai;E. Nakai;Gaku Sadasue
众所周知，基于具有Varopoulos维的对称马尔可夫半群的分数次积分算子α是有界的，如果0<；α<；d，1<；p<；q<；∞和−d/p+α=−d/q，就像定义在二维欧氏空间上的通常的分数次积分算子一样。我们引入了基于对称马氏半群的广义分数次积分算子，并将Lp-Lq有界性推广到Orlicz空间。我们还将结果应用于与Heisenberg群上的次拉普拉斯算子所生成的扩散过程有关的半群。此外，我们还给出了广义分数次积分算子在齐型空间上有界性的充要条件，并将其应用于Heisenberg群。
It is known that the fractional integral operatorIαbased on a symmetric Markovian semigroup with Varopoulos dimensiondis bounded fromLptoLq, if 0 <α<d, 1 <p<q< ∞ and −d/p+α= −d/q, like the usual fractional integral operator defined on theddimensional Euclidean space. We introduce generalized fractional integral operators based on symmetric Markovian semigroups and extend theLp-Lqboundedness to Orlicz spaces. We also apply the result to the semigroup associated with the diffusion process generated by the sub-Laplacian on the Heisenberg group. Moreover, we show necessary and sufficient conditions for the boundedness of the generalized fractional integral operator on the space of homogeneous type and apply them to the Heisenberg group.