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

Stefan Richter; Brett D. Wick

Concrete Operators (2016)

  • Volume: 3, Issue: 1, page 25-28
  • ISSN: 2299-3282

Abstract

top
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.

How to cite

top

Stefan Richter, and Brett D. Wick. "A remark on the multipliers on spaces of Weak Products of functions." Concrete Operators 3.1 (2016): 25-28. <http://eudml.org/doc/277107>.

@article{StefanRichter2016,
abstract = {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.},
author = {Stefan Richter, Brett D. Wick},
journal = {Concrete Operators},
keywords = {Dirichlet space; Drury-Arveson space; Weak product; Multiplier; weak product; multiplier},
language = {eng},
number = {1},
pages = {25-28},
title = {A remark on the multipliers on spaces of Weak Products of functions},
url = {http://eudml.org/doc/277107},
volume = {3},
year = {2016},
}

TY - JOUR
AU - Stefan Richter
AU - Brett D. Wick
TI - A remark on the multipliers on spaces of Weak Products of functions
JO - Concrete Operators
PY - 2016
VL - 3
IS - 1
SP - 25
EP - 28
AB - 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.
LA - eng
KW - Dirichlet space; Drury-Arveson space; Weak product; Multiplier; weak product; multiplier
UR - http://eudml.org/doc/277107
ER -

References

top
  1. [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.  Zbl1262.30066
  2. [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. [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.  Zbl1276.30063
  4. [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.  Zbl1217.47058
  5. [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.  Zbl0326.32011
  6. [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.  Zbl1331.47037
  7. [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.  Zbl1343.46022
  8. [8] Ortega, Joaquín and Fàbrega, Joan, Multipliers in Hardy-Sobolev spaces, Integral Equations Operator Theory, 55, 2006, no. 4, 535–560.  
  9. [9] Richter, Stefan and Sundberg, Carl, Weak products of Dirichlet functions, J. Funct. Anal., 266, 2014, no. 8, 5270–5299.  Zbl1303.30050
  10. [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.  Zbl06560782

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.