[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b180501

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)

Publication Information

Bulletin of the Korean Mathematical Society / v.56, no.3, 2019 , pp. 691-702 More about this Journal

Abstract

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

Keywords

coefficient multiplication operators; Dirichlet spaces;

Citations & Related Records

Reference

1	M. Jevtic and I. Jovanovic, Coefficient multipliers of mixed norm spaces, Canad. Math. Bull. 36 (1993), no. 3, 283-285. DOI
2	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.
3	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.
4	Z. Lou, Coefficient multipliers of Bergman spaces $A^p$ . II, Canad. Math. Bull. 40 (1997), no. 4, 475-487. DOI
5	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. DOI
6	M. Mateljevic and M. Pavlovic, Multipliers of $H^p$ and BMOA, Pacific J. Math. 146 (1990), no. 1, 71-84. DOI
7	M. Pavlovic, Introduction to Function Spaces on the Disk, Posebna Izdanja, 20, Matematicki Institut SANU, Belgrade, 2004.
8	P. Wojtaszczyk, On multipliers into Bergman spaces and Nevanlinna class, Canad. Math. Bull. 33 (1990), no. 2, 151-161. DOI
9	X. Yue, Coefficient multipliers on weighted Bergman spaces, Complex Var. Elliptic Equ. 40 (1999), no. 2, 163-172. DOI
10	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).
11	K. H. Zhu, Duality and Hankel operators on the Bergman spaces of bounded symmetric domains, J. Funct. Anal. 81 (1988), no. 2, 260-278. DOI
12	Blasco and M. Pavlovic, Coefficient multipliers on Banach spaces of analytic functions, Rev. Mat. Iberoam. 27 (2011), no. 2, 415-447. DOI
13	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. DOI
14	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. DOI
15	P. L. Duren, Theory of $H^p$ Spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York, 1970.
16	T. M. Flett, The dual of an inequality of Hardy and Littlewood and some related inequalities, J. Math. Anal. Appl. 38 (1972), 746-765. DOI
17	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.