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Projections in weighted spaces, skew projections and inversion of Toeplitz operators

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Abstract

In many cases the self-adjoint projection of a Lebesgue space L2(dx) onto a closed subspace is also bounded on a weighted space L2(wdx) . Our main result is that in this case certain self-adjoint projections on weighted spaces are bounded on L2(dx) . The analysis also produces an invertibility criterion for certain Toeplitz operators. The proof is based on analysis of a perturbation series and hence is valid in fairly general circumstances.

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Authors and Affiliations

  1. Department of Mathematics, Yale University, 06520, New Haven, CT, USA

    R. R. Coifman

  2. Department of Mathematics, Washington University, 63130, St. Louis, MO, USA

    R. Rochberg

Authors
  1. R. R. Coifman
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  2. R. Rochberg
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Both authors supported in part by grants from the National Science Foundation.

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Coifman, R.R., Rochberg, R. Projections in weighted spaces, skew projections and inversion of Toeplitz operators. Integr equ oper theory 5, 145–159 (1982). https://doi.org/10.1007/BF01694036

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  • DOI: https://doi.org/10.1007/BF01694036

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