A remark on the multipliers on spaces of Weak Products of functions

• Autorzy: Stefan Richter , Brett D. Wick
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Dirichlet space; Drury-Arveson space; Weak product; Multiplier

• Wydawca: De Gruyter Open
• Czasopismo: Concrete Operators
• Rocznik: 2016
• Tom: 3
• Numer: 1
• Strony: 25-28

Daty

otrzymano

2015-10-30

zaakceptowano

2016-01-27

online

2016-04-12

Twórcy

autor

Stefan Richter

• Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA

autor

Brett D. Wick

• Department of Mathematics, Washington University – St. Louis, St. Louis, MO 63130, USA and School of Mathematics, Georgia Institute of Technology, Atlanta GA 30332-0160, USA

Bibliografia

• [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.
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• [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.
• [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.
• [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.
• [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.
• [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.
• [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.
• [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.

Identyfikatory

DOI

10.1515/conop-2016-0004