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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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