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Invertibility of some singular integral operators and a lifting theorem

Invertibility of some singular integral operators and a lifting theorem

Let P_{+} be an analytic projection and let P_{-} be a co analytic projection.Let L^{2}(W) be the usual weighted Lebesgue space on the unit circle.For some weight W. P_{+} is not continuous in the norm of L^{2}(W) .We shall define the Hilbert space L^{2}((W)) such that for any weight W, …