BOUNDEDNESS OF MAXIMAL FUNCTIONS ON NONDOUBLING PARABOLIC MANIFOLDS WITH ENDS
BOUNDEDNESS OF MAXIMAL FUNCTIONS ON NONDOUBLING PARABOLIC MANIFOLDS WITH ENDS
复制标题
有端非重抛物流形上极大函数的有界性
DOI：
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发表时间：
2020
影响因子：
0.7
通讯作者：
Hong Chuong Doan
中科院分区：
文献类型：
--
作者：
Hong Chuong Doan
Abstract Let $M$ be a nondoubling parabolic manifold with ends. First, this paper investigates the boundedness of the maximal function associated with the heat semigroup ${mathcal{M}}_{unicode[STIX]{x1D6E5}}f(x):=sup _{t>0}|e^{-tunicode[STIX]{x1D6E5}}f(x)|$ where $unicode[STIX]{x1D6E5}$ is the Laplace–Beltrami operator acting on $M$ . Then, by combining the subordination formula with the previous result, we obtain the weak type $(1,1)$ and $L^{p}$ boundedness of the maximal function ${mathcal{M}}_{sqrt{L}}^{k}f(x):=sup _{t>0}|(tsqrt{L})^{k}e^{-tsqrt{L}}f(x)|$ on $L^{p}(M)$ for $1<pleq infty$ where $k$ is a nonnegative integer and $L$ is a nonnegative self-adjoint operator satisfying a suitable heat kernel upper bound. An interesting thing about the results is the lack of both doubling condition of $M$ and the smoothness of the operators’ kernels.
Abstract Let $M$ be a nondoubling parabolic manifold with ends. First, this paper investigates the boundedness of the maximal function associated with the heat semigroup ${mathcal{M}}_{unicode[STIX]{x1D6E5}}f(x):=sup _{t>0}|e^{-tunicode[STIX]{x1D6E5}}f(x)|$ where $unicode[STIX]{x1D6E5}$ is the Laplace–Beltrami operator acting on $M$ . Then, by combining the subordination formula with the previous result, we obtain the weak type $(1,1)$ and $L^{p}$ boundedness of the maximal function ${mathcal{M}}_{sqrt{L}}^{k}f(x):=sup _{t>0}|(tsqrt{L})^{k}e^{-tsqrt{L}}f(x)|$ on $L^{p}(M)$ for $1<pleq infty$ where $k$ is a nonnegative integer and $L$ is a nonnegative self-adjoint operator satisfying a suitable heat kernel upper bound. An interesting thing about the results is the lack of both doubling condition of $M$ and the smoothness of the operators’ kernels.
DOI：
10.1016/j.matpur.2018.03.002
发表时间：
2018
期刊：
Journal de Mathématiques Pures et Appliquées
影响因子：
--
作者：
Grigor'yan, Alexander;Ishiwata, Satoshi;Saloff-Coste, Laurent
通讯作者：
Saloff-Coste, Laurent