대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제47권3호
  • /
  • Pages.527-540
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  • 2010
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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A WEIGHTED COMPOSITION OPERATOR ON THE LOGARITHMIC BLOCH SPACE

  • Ye, Shanli (Department of Mathematics Fujian Normal University)
  • 투고 : 2008.12.03
  • 발행 : 2010.05.31
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초록

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 ${\mathcal{L}\ss_0$.

키워드

참고문헌

  1. L. Brown and A. L. Shields, Multipliers and cyclic vectors in the Bloch space, Michigan Math. J. 38 (1991), no. 1, 141-146. https://doi.org/10.1307/mmj/1029004269
  2. C. C. Cowen and B. D. Maccluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1995.
  3. K. Madigan, Composition operators on analytic Lipschitz spaces, Proc. Amer. Math. Soc. 119 (1993), no. 2, 465-473. https://doi.org/10.2307/2159930
  4. K. Madigan and A. Matheson, Compact composition operators on the Bloch space, Trans. Amer. Math. Soc. 347 (1995), no. 7, 2679-2687. https://doi.org/10.2307/2154848
  5. S. Ohno, K. Stroethoff, and R. H. Zhao, Weighted composition operators between Blochtype spaces, Rocky Mountain J. Math. 33 (2003), no. 1, 191-215. https://doi.org/10.1216/rmjm/1181069993
  6. S. Ohno and R. H. Zhao, Weighted composition operators on the Bloch space, Bull. Austral. Math. Soc. 63 (2001), no. 2, 177-185. https://doi.org/10.1017/S0004972700019250
  7. J. H. Shapiro, Composition Operators and Classical Function Theory, Universitext: Tracts in Mathematics. Springer-Verlag, New York, 1993.
  8. W. Smith, Composition operators between Bergman and Hardy spaces, Trans. Amer. Math. Soc. 348 (1996), no. 6, 2331-2348. https://doi.org/10.1090/S0002-9947-96-01647-9
  9. K. Stroethoff, Besov-type characterisations for the Bloch space, Bull. Austral. Math. Soc. 39 (1989), no. 3, 405-420. https://doi.org/10.1017/S0004972700003324
  10. S. L. Ye, Multipliers and cyclic vectors on the weighted Bloch space, Math. J. Okayama Univ. 48 (2006), 135-143.
  11. S. L. Ye, Weighted composition operators from F(p, q, s) into logarithmic Bloch space, J. Korean Math. Soc. 45 (2008), no. 4, 977-991. https://doi.org/10.4134/JKMS.2008.45.4.977
  12. R. Yoneda, The composition operators on weighted Bloch space, Arch. Math. (Basel) 78 (2002), no. 4, 310-317. https://doi.org/10.1007/s00013-002-8252-y
  13. R. Zhao, Composition operators from Bloch type spaces to Hardy and Besov spaces, J. Math. Anal. Appl. 233 (1999), no. 2, 749-766. https://doi.org/10.1006/jmaa.1999.6341
  14. K. H. Zhu, Bloch type spaces of analytic functions, Rocky Mountain J. Math. 23 (1993), no. 3, 1143-1177. https://doi.org/10.1216/rmjm/1181072549
  15. K. H. Zhu, Operator Theory in Function Spaces, Monographs and Textbooks in Pure and Applied Mathematics, 139. Marcel Dekker, Inc., New York, 1990.

피인용 문헌

  1. On a Stević-Sharma operator from Hardy spaces to the logarithmic Bloch spaces vol.2015, pp.1, 2015, https://doi.org/10.1186/s13660-015-0547-1
  2. Weighted Composition Operators on the Zygmund Space vol.2012, 2012, https://doi.org/10.1155/2012/462482
  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