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- W1966150728 abstract "ABSTRACT. For a large class of bounded domains in C, we describe thosefinite codimensional subspaces of the Bergman space that are invariant undermultiplication by z. Using different techniques for certain domains in CN, wedescribe those finite codimensional subspaces of the Bergman space that areinvariant under multiplication by all the coordinate functions. Fix a positive integer N, and let V denote Lebesgue volume measure on CN (sothat if N = 1, then V is just area measure). Let Q c C^ be a domain, which, asusual, means that 0 is a nonempty open connected subset of C^. For / an analyticfunction from 0 to C and 1 < p < oo, the norm ||/||n,P is defined by Wfh,r=(jnfpdV The Bergman space L^(Q) is defined to be the set of analytic functions from fi toC such that ||/||n,P < oo. Our goal in this paper is to describe the closed finite codimensional subspaces ofLpa (0) that are invariant under multiplication by the coordinate functions zi,...," @default.
- W1966150728 created "2016-06-24" @default.
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- W1966150728 date "1988-02-01" @default.
- W1966150728 modified "2023-09-25" @default.
- W1966150728 title "Finite-codimensional invariant subspaces of Bergman spaces" @default.
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- W1966150728 doi "https://doi.org/10.1090/s0002-9947-1988-0933319-5" @default.
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