Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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COEFFICIENT MULTIPLIERS ON DIRICHLET TYPE SPACES

  • Li, Dongxing (Department of Mathematics Shantou University) ;
  • Wulan, Hasi (Department of Mathematics Shantou University) ;
  • Zhao, Ruhan (Department of Mathematics SUNY Brockport)
  • Received : 2018.05.25
  • Accepted : 2018.10.29
  • Published : 2019.05.31
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Abstract

We characterize coefficient multipliers from certain Dirichlet type spaces to Hardy spaces and weighted Bergman spaces.

Keywords

Acknowledgement

Supported by : China National Natural Science Foundation, Natural Science Foundation of Guangdong Province

References

  1. Blasco and M. Pavlovic, Coefficient multipliers on Banach spaces of analytic functions, Rev. Mat. Iberoam. 27 (2011), no. 2, 415-447. https://doi.org/10.4171/RMI/642
  2. S. M. Buckley, P. Koskela, and D. Vukotic, Fractional integration, differentiation, and weighted Bergman spaces, Math. Proc. Cambridge Philos. Soc. 126 (1999), no. 2, 369-385. https://doi.org/10.1017/S030500419800334X
  3. S. M. Buckley, M. S. Ramanujan, and D. Vukotic, Bounded and compact multipliers between Bergman and Hardy spaces, Integral Equations Operator Theory 35 (1999), no. 1, 1-19. https://doi.org/10.1007/BF01225524
  4. P. L. Duren, Theory of $H^p$ Spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York, 1970.
  5. T. M. Flett, The dual of an inequality of Hardy and Littlewood and some related inequalities, J. Math. Anal. Appl. 38 (1972), 746-765. https://doi.org/10.1016/0022-247X(72)90081-9
  6. G. H. Hardy and J. E. Littlewood, Theorems concerning mean values of analytic or harmonic functions, Quart. J. Math., Oxford Ser. 12 (1941), 221-256.
  7. M. Jevtic and I. Jovanovic, Coefficient multipliers of mixed norm spaces, Canad. Math. Bull. 36 (1993), no. 3, 283-285. https://doi.org/10.4153/CMB-1993-040-2
  8. M. Jevtic, D. Vukotic, and M. Arsenovic, Taylor coefficients and coefficient multipliers of Hardy and Bergman-type spaces, RSME Springer Series, 2, Springer, Cham, 2016.
  9. J. E. Littlewood and R. E. A. C. Paley, Theorems on Fourier series and power series (II), Proc. London Math. Soc. (2) 42 (1936), no. 1, 52-89.
  10. Z. Lou, Coefficient multipliers of Bergman spaces $A^p$. II, Canad. Math. Bull. 40 (1997), no. 4, 475-487. https://doi.org/10.4153/CMB-1997-057-1
  11. M. Mateljevic and M. Pavlovic, $L^p$-behavior of power series with positive coefficients and Hardy spaces, Proc. Amer. Math. Soc. 87 (1983), no. 2, 309-316. https://doi.org/10.2307/2043708
  12. M. Mateljevic and M. Pavlovic, Multipliers of $H^p$ and BMOA, Pacific J. Math. 146 (1990), no. 1, 71-84. https://doi.org/10.2140/pjm.1990.146.71
  13. M. Pavlovic, Introduction to Function Spaces on the Disk, Posebna Izdanja, 20, Matematicki Institut SANU, Belgrade, 2004.
  14. P. Wojtaszczyk, On multipliers into Bergman spaces and Nevanlinna class, Canad. Math. Bull. 33 (1990), no. 2, 151-161. https://doi.org/10.4153/CMB-1990-026-7
  15. X. Yue, Coefficient multipliers on weighted Bergman spaces, Complex Var. Elliptic Equ. 40 (1999), no. 2, 163-172. https://doi.org/10.1080/17476939908815216
  16. R. Zhao and K. Zhu, Theory of Bergman spaces in the unit ball of $\mathbb{C}^n$, Mem. Soc. Math. Fr. (N.S.) No. 115 (2008), vi+103 pp. (2009).
  17. K. H. Zhu, Duality and Hankel operators on the Bergman spaces of bounded symmetric domains, J. Funct. Anal. 81 (1988), no. 2, 260-278. https://doi.org/10.1016/0022-1236(88)90100-0