Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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EXTENDED CESÀRO OPERATORS BETWEEN α-BLOCH SPACES AND QK SPACES

  • Wang, Shunlai (School of Mathematics and Statistics Nanjing University of Information Science and Technology) ;
  • Zhang, Taizhong (School of Mathematics and Statistics Nanjing University of Information Science and Technology)
  • Received : 2016.06.09
  • Accepted : 2016.09.26
  • Published : 2017.07.31
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Abstract

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.

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References

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