… Toeplitz operators which will play the dominant part in this book. Having identified the local
spectra of Toeplitz operators, … of extending Carleson curves and Muckenhout weights in order …

… curve Γ is nice and ω is an arbitrary Muckenhoupt weight, … Carleson curves with nice weights.
In this paper we show that for general Carleson curves and general Muckenhoupt weights …

… symbols and of singular integral operators with piecewise continuous coefficients on Carleson
curves with Muckenhoupt weights. A locally rectifiable curve Γ is a Carleson curve if ε−"QΓ…

… Two basic theorems on invertibility and Fredholmness of Toeplitz operators We start with
two well known results on invertibility and Fredholmness of Toeplitz operators (see eg [1, …

… The book under review is devoted to the spectral theory of Toeplitz operators with
piecewise continuous symbols and of singular integral operators with piecewise continuous …

… by the behavior of the curve and in no way tied in with the presence of a weight, The subject
of … for Toeplitz operators, We will embark on spaces with general Muckenhoupt weights (and …

Chapter 1 Carleson curves Page 1 Chapter 1 Carleson curves The purpose of this chapter
is to acquaint the reader with some simple but basic properties of Carleson curves and to …

… From now on we always assume that 1 < p < 0% that P is a closed Carleson curve, and that
w is a Muckenhoupt weight in Ap(F). Once Lemma 2.1 is available one may proceed as in [15…

… Carleson then constant weights belong to Ap(f). Therefore, when dealing with Muckenhoupt
weights we will henceforth always assume that the underlying curve is a Carleson curve. In …

… r be a Carleson Jordan curve, and let w be a weight in Ap(r). We know that then the operator
8 is … In the next section we show that equality in (6.5) holds whenever f is a Carleson curve. …