| Singular Integral Operators on New BMO and Lipschitz Spaces of Homogeneous Type |
| Received:January 17, 2015 Revised:May 27, 2015 |
| Key Words:
singular integral operators BMO spaces Lipschitz spaces heat kernel spaces of homogeneous type
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11261055; 11161044). |
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| Abstract: |
| Let $(X,d,\mu)$ be a space of homogeneous type, ${\rm BMO}_A(X)$ and ${\rm Lip}_A(\beta,X)$ be the space of BMO type, lipschitz type associated with an approximation to the identity $\{A_t\}_{t>0}$ and introduced by Duong, Yan and Tang, respectively. Assuming that $T$ is a bounded linear operator on $L^2(X)$, we find the sufficient condition on the kernel of $T$ so that $T$ is bounded from ${\rm BMO}(X)$ to ${\rm BMO}_A(X)$ and from ${\rm Lip}(\beta, X)$ to ${\rm Lip}_A(\beta,X)$. As an application, the boundedness of Calder\'on-Zygmund operators with nonsmooth kernels on ${\rm BMO}(\mathbb{R}^n)$ and ${\rm Lip}(\beta, \mathbb{R}^n)$ are also obtained. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2016.01.012 |
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