DOI QR코드

DOI QR Code

PRODUCTS OF DIFFERENTIATION AND COMPOSITION ON BLOCH SPACES

  • Ohno, Shuichi
  • Published : 2009.11.30

Abstract

We will consider the questions of when the products of composition and differentiation are bounded and compact on Bloch and little Bloch spaces.

Keywords

differentiation;composition operators;Bloch spaces

References

  1. A. B. Aleksandrov, J. M. Anderson, and A. Nicolau, Inner functions, Bloch spaces and symmetric measures, Proc. London Math. Soc. (3) 79 (1999), no. 2, 318-352 https://doi.org/10.1112/S002461159901196X
  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. P. L. Duren, Theory of $H^p$ Spaces, Academic Press, New York, 1970
  4. S. Ohno, K. Stroehoff, and R. Zhao, Weighted composition operators between Bloch-type spaces, Rocky Mountain J. Math. 33 (2003), no. 1, 191-215 https://doi.org/10.1216/rmjm/1181069993
  5. J. H. Shapiro, Composition Operators and Classical Function Theory, Springer-Verlag, New York, 1993
  6. 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
  7. K. Zhu, Operator Theory in Function Spaces, Marcel Dekker, New York, 1990
  8. R. A. Hibschweiler and N. Portnoy, Composition followed by differentiation between Bergman and Hardy spaces, Rocky Mountain J. Math. 35 (2005), no. 3, 843-855 https://doi.org/10.1216/rmjm/1181069709
  9. S. Ohno, Products of composition and differentiation between Hardy spaces, Bull. Austral. Math. Soc. 73 (2006), no. 2, 235-243 https://doi.org/10.1017/S0004972700038818

Cited by

  1. Product-type operators from Zygmund spaces to Bloch-Orlicz spaces vol.62, pp.11, 2017, https://doi.org/10.1080/17476933.2016.1278436
  2. Weighted composition followed by differentiation between Bloch-type spaces vol.27, pp.2, 2014, https://doi.org/10.1007/s13163-013-0138-y
  3. New characterizations for the products of differentiation and composition operators between Bloch-type spaces vol.2014, pp.1, 2014, https://doi.org/10.1186/1029-242X-2014-502
  4. Characterizations of composition followed by differentiation between Bloch-type spaces vol.218, pp.8, 2011, https://doi.org/10.1016/j.amc.2011.10.004
  5. Weighted Differentiation Composition Operators to Bloch-Type Spaces vol.2013, 2013, https://doi.org/10.1155/2013/151929
  6. Products of Composition and Differentiation Operators from Bloch intoQKSpaces vol.2016, 2016, https://doi.org/10.1155/2016/5084794
  7. Product-Type Operators from Logarithmic Bergman-Type Spaces to Zygmund–Orlicz Spaces vol.13, pp.6, 2016, https://doi.org/10.1007/s00009-016-0767-8
  8. Weighted differentiation composition operators from the logarithmic Bloch space to the weighted-type space vol.24, pp.3, 2016, https://doi.org/10.1515/auom-2016-0056
  9. Generalized weighted composition operators from the F(p,q,s) space to the Bloch-type space vol.218, pp.9, 2012, https://doi.org/10.1016/j.amc.2011.10.062
  10. Weighted iterated radial operators between different weighted Bergman spaces on the unit ball vol.218, pp.17, 2012, https://doi.org/10.1016/j.amc.2012.01.052
  11. Generalized weighted composition operators from Zygmund spaces to Bloch–Orlicz type spaces vol.273, 2016, https://doi.org/10.1016/j.amc.2015.09.055
  12. Generalized product-type operators from weighted Bergman–Orlicz spaces to Bloch–Orlicz spaces vol.268, 2015, https://doi.org/10.1016/j.amc.2015.06.100
  13. PRODUCT-TYPE OPERATORS FROM WEIGHTED BERGMAN-ORLICZ SPACES TO WEIGHTED ZYGMUND SPACES vol.52, pp.4, 2015, https://doi.org/10.4134/BKMS.2015.52.4.1383
  14. On a product-type operator from weighted Bergman–Orlicz space to some weighted type spaces vol.256, 2015, https://doi.org/10.1016/j.amc.2015.01.025
  15. Weighted radial operator from the mixed-norm space to the nth weighted-type space on the unit ball vol.218, pp.18, 2012, https://doi.org/10.1016/j.amc.2012.03.001
  16. On an integral-type operator from the Bloch space to mixed norm spaces vol.273, 2016, https://doi.org/10.1016/j.amc.2015.10.022
  17. On a product operator from weighted Bergman-Nevanlinna spaces to weighted Zygmund spaces vol.2014, pp.1, 2014, https://doi.org/10.1186/1029-242X-2014-404
  18. Generalized composition operators on weighted Hardy spaces vol.218, pp.17, 2012, https://doi.org/10.1016/j.amc.2012.01.061
  19. On Stević-Sharma operator from the Zygmund space to the Bloch-Orlicz space vol.2015, pp.1, 2015, https://doi.org/10.1186/s13662-015-0567-7
  20. Iterated differentiation followed by composition from Bloch-type spaces to weighted BMOA spaces vol.218, pp.7, 2011, https://doi.org/10.1016/j.amc.2011.08.103
  21. Sums of Weighted Differentiation Composition Operators pp.1661-8262, 2019, https://doi.org/10.1007/s11785-019-00891-5