If H denotes a Hilbert space of analytic functions on a region Ω ⊆ Cd , then the weak product is defined by [...] We prove that if H is a first order holomorphic Besov Hilbert space on the unit ball of Cd , then the multiplier algebras of H and of H ⊙ H coincide.
@article{bwmeta1.element.doi-10_1515_conop-2016-0004,
author = {Stefan Richter and Brett D. Wick},
title = {A remark on the multipliers on spaces of Weak Products of functions},
journal = {Concrete Operators},
volume = {3},
year = {2016},
pages = {25-28},
zbl = {1344.47024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_conop-2016-0004}
}
Stefan Richter; Brett D. Wick. A remark on the multipliers on spaces of Weak Products of functions. Concrete Operators, Tome 3 (2016) pp. 25-28. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_conop-2016-0004/
[1] Arcozzi, Nicola and Rochberg, Richard and Sawyer, Eric and Wick, Brett D., Bilinear forms on the Dirichlet space, Anal. PDE, 3, 2010, no. 1, 21–47. | Zbl 1262.30066
[2] Beatrous, Frank and Burbea, Jacob, Holomorphic Sobolev spaces on the ball, Dissertationes Math. (Rozprawy Mat.), Polska Akademia Nauk. Instytut Matematyczny. Dissertationes Mathematicae. Rozprawy Matematyczne, 276, 1989.
[3] Cascante, Carme and Ortega, Joaquin M., On a characterization of bilinear forms on the Dirichlet space, Proc. Amer. Math. Soc., 140, 2012, no. 7, 2429–2440. | Zbl 1276.30063
[4] Cascante, Carme and Fàbrega, Joan and Ortega, Joaquín M., On weighted Toeplitz, big Hankel operators and Carleson measures, Integral Equations Operator Theory, 66, 2010, no.4, 495–528. | Zbl 1217.47058
[5] Coifman, R. R. and Rochberg, R. and Weiss, Guido, Factorization theorems for Hardy spaces in several variables, Ann. of Math. (2) , 103, 1976, no. 3, 611–635. | Zbl 0326.32011
[6] Luo, Shuaibing and Richter, Stefan, Hankel operators and invariant subspaces of the Dirichlet space, J. Lond. Math. Soc. (2), 91, 2015, no. 2, 423–438. | Zbl 1331.47037
[7] Luo, Shuaibing, On the Index of Invariant Subspaces in the Space of Weak Products of Dirichlet Functions, Complex Anal. Oper. Theory, 9, 2015, no. 6, 1311–1323. | Zbl 1343.46022
[8] Ortega, Joaquín and Fàbrega, Joan, Multipliers in Hardy-Sobolev spaces, Integral Equations Operator Theory, 55, 2006, no. 4, 535–560.
[9] Richter, Stefan and Sundberg, Carl, Weak products of Dirichlet functions, J. Funct. Anal., 266, 2014, no. 8, 5270–5299. | Zbl 1303.30050
[10] Richter, Stefan and Sunkes, James, Hankel operators, Invariant subspaces, and cyclic vectors in the Drury-Arveson space, Proc. Amer. Math. Soc., Proc. Amer. Math. Soc., to appear. | Zbl 06560782