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A WEIGHTED COMPOSITION OPERATOR ON THE LOGARITHMIC BLOCH SPACE

  • Ye, Shanli (Department of Mathematics Fujian Normal University)
  • Received : 2008.12.03
  • Published : 2010.05.31

Abstract

We characterize the boundedness and compactness of the weighted composition operator on the logarithmic Bloch space $\mathcal{L}\ss=\{f{\in}H(D):sup_D(1-|z|^2)ln(\frac{2}{1-|z|})|f'(z)|$<+$\infty$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$. The results generalize the known corresponding results on the composition operator and the pointwise multiplier on the logarithmic Bloch space ${\mathcal{L}\ss$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$.

Keywords

logarithmic Bloch space;weighted composition operator;boundedness;compactness

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  3. Logarithmic Bloch spaces and their weighted composition operators vol.65, pp.1, 2016, https://doi.org/10.1007/s12215-015-0226-6
  4. Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces vol.2012, 2012, https://doi.org/10.1155/2012/454820
  5. Weighted Composition Operators from Hardy to Zygmund Type Spaces vol.2013, 2013, https://doi.org/10.1155/2013/365286
  6. Norm and Essential Norm of Composition Followed by Differentiation from Logarithmic Bloch Spaces to Hμ∞ vol.2014, 2014, https://doi.org/10.1155/2014/725145