Boundedness of the Riesz projection on spaces with weights

Abstract

Let ∂D be the unit circle in the complex plane, define the function χ on ∂D by χ(eiθ) = eiθ, and set P = {p : p = ∑Nk=−N ckχ}. Let σ be normalized Lebesgue measure on ∂D. The Riesz projection P+ is defined on P by the formula P+( ∑N k=−N ckχ k) = ∑N k=0 ckχ k. In [4], Paul Koosis proved: Theorem 1 (Koosis). Given a non-negative function w ∈ L1, there exists a non-negative, non-trivial function v ∈ L1 such that ∫