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Search: MSC category 47B07 ( Operators defined by compactness properties )

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1. CJM Online first

Guo, Xiaoli; Hu, Guoen
On the commutators of singular integral operators with rough convolution kernels
Let $T_{\Omega}$ be the singular integral operator with kernel $\frac{\Omega(x)}{|x|^n}$, where $\Omega$ is homogeneous of degree zero, has mean value zero and belongs to $L^q(S^{n-1})$ for some $q\in (1,\,\infty]$. In this paper, the authors establish the compactness on weighted $L^p$ spaces, and the Morrey spaces, for the commutator generated by $\operatorname{CMO}(\mathbb{R}^n)$ function and $T_{\Omega}$. The associated maximal operator and the discrete maximal operator are also considered.

Keywords:commutator, singular integral operator, compact operator, completely continuous operator, maximal operator, Morrey space
Categories:42B20, 47B07

2. CJM 2011 (vol 63 pp. 862)

Hosokawa, Takuya; Nieminen, Pekka J.; Ohno, Shûichi
Linear Combinations of Composition Operators on the Bloch Spaces
We characterize the compactness of linear combinations of analytic composition operators on the Bloch space. We also study their boundedness and compactness on the little Bloch space.

Keywords: composition operator, compactness, Bloch space
Categories:47B33, 30D45, 47B07

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