• Korean Journal of Mathematics
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• v.25 no.1
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• pp.117-126
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• 2017

The subnormality of some classes of operators is a very interesting property. In this paper, we prove that the weighted $Ces{\grave{a}}ro$ operator $C_h{\in}{\ell}^2(h)$ is subnormal and we described completely the set of the extended eigenvalues for the weighted $Ces{\grave{a}}ro$ operator, some other important results are also given.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.567-578
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• 2017

Many scholars studied the boundedness of $Ces{\grave{a}}ro$ operators between $Q_K$ spaces and Bloch spaces of holomorphic functions in the unit disc in the complex plane, however, they did not describe the compactness. Let 0 < ${\alpha}$ < $+{\infty}$, K(r) be right continuous nondecreasing functions on (0, $+{\infty}$) and satisfy $${\displaystyle\smashmargin{2}{\int\nolimits_0}^{\frac{1}{e}}}K({\log}{\frac{1}{r}})rdr<+{\infty}$$. Suppose g is a holomorphic function in the unit disk. In this paper, some sufficient and necessary conditions for the extended $Ces{\grave{a}}ro$ operators $T_g$ between ${\alpha}$-Bloch spaces and $Q_K$ spaces in the unit disc to be bounded and compact are obtained.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.57-66
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• 2009

In this paper, we characterize the boundedness and compactness of the extended $Ces{\grave{a}}ro$ operators from general function spaces F(p, q, s) to Bloch-type spaces ${\mathcal{B}}_{\mu}$ where $\mu$ is normal function on [0,1).