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Hankel- and Toeplitz-Type Operators on the Unit Ball

โœ Scribed by Jianxun He

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
129 KB
Volume
259
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

Let B m be the unit ball in the m-dimensional complex plane C m with the weighted measure

From the viewpoint of the Cauchy-Riemann operator we give an orthogonal direct sum decomposition for L 2 B m dยต ฮฑ z , i.e., L 2 B m dยต ฮฑ z = โŠ• nโˆˆZ + ฯƒโˆˆ A ฯƒ n , where the components A + + + 0 and A ---0 are just the weighted Bergman and conjugate Bergman spaces, respectively. Using the simplex polynomials from T. H. Koornwinder and A. L. Schwartz (1997, Constr. Approx 13, 537-567), we obtain an orthogonal basis for every subspace. As an application of the orthogonal decomposition, we define the Hankel-and Toeplitz-type operators and discuss S p -criteria for these kinds of operators.

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