Abstract
In this chapter we prove that if Γ is a Carleson curve and w is a weight in A P (Γ) (1 <p < ∞), then the Cauchy singular integral operator S is bounded on L P(Γ,w). There are now various proofs of this deep result, and the proof given in the following is certainly not the most elegant proof. However, it is reasonably self-contained and it contains several details which are usually disposed of as “standard” and are therefore omitted in the advanced texts on this topic.
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© 1997 Springer Basel AG
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Böttcher, A., Karlovich, Y.I. (1997). Weighted norm inequalities. In: Carleson Curves, Muckenhoupt Weights, and Toeplitz Operators. Progress in Mathematics, vol 154. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8922-3_5
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DOI: https://doi.org/10.1007/978-3-0348-8922-3_5
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9828-7
Online ISBN: 978-3-0348-8922-3
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