Toeplitz operators and Carleson measures in strongly pseudoconvex domains
Copyright policy )Toeplitz operators and Carleson measures in strongly pseudoconvex domains
We study mapping properties of Toeplitz operators associated to a finite positive Borel measure on a bounded strongly pseudoconvex domain D in n complex variables. In particular, we give sharp conditions on the measure ensuring that the associated Toeplitz operator maps the Bergman space A^p(D) into A^r(D) with r>p, generalizing and making more precise results by Cuckovic and McNeal. To do so, we give a geometric characterization of Carleson measures and of vanishing Carleson measures of weighted Bergman spaces in terms of the intrinsic Kobayashi geometry of the domain, generalizing to this setting results obtained by Kaptanoglu for the unit ball.
36 pages
- University of Parma Italy
- University of Milan Italy
- University of Milano-Bicocca Italy
- University of Pisa Italy
Mathematics - Complex Variables, Weighted Bergman space, Bergman spaces of functions in several complex variables, Strongly pseudoconvex domains, 510, weighted Bergman space, Functional Analysis (math.FA), Mathematics - Functional Analysis, Toeplitz operator, Toeplitz operators, Hankel operators, Wiener-Hopf operators, FOS: Mathematics, 32A36 (Primary) 47B35, 46E15, 46E22, 32A25, 32Q45, 32T15 (Secondary), Strongly pseudoconvex domain, Carleson measure, strongly pseudoconvex domain, Complex Variables (math.CV), Analysis
Mathematics - Complex Variables, Weighted Bergman space, Bergman spaces of functions in several complex variables, Strongly pseudoconvex domains, 510, weighted Bergman space, Functional Analysis (math.FA), Mathematics - Functional Analysis, Toeplitz operator, Toeplitz operators, Hankel operators, Wiener-Hopf operators, FOS: Mathematics, 32A36 (Primary) 47B35, 46E15, 46E22, 32A25, 32Q45, 32T15 (Secondary), Strongly pseudoconvex domain, Carleson measure, strongly pseudoconvex domain, Complex Variables (math.CV), Analysis
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