Mapping properties of some singular operators in Besov type subspaces of \(C(-1,1)\) (Q2501053)

The paper deals with singular integral operators \[ (A^{\alpha,\beta}f)(y)=\cos(\alpha\pi)v^{\alpha,\beta}(y)f(y)-\frac{\sin(\alpha\pi)}{\pi}\int_{-1}^1 f(x)\frac{v^{\alpha,\beta}(x)}{x-y}\,dx,\quad y\in(-1,1), \] where \(v^{\alpha,\beta}(x)=(1-x)^\alpha(1+x)^\beta\) is a Jacobi weight with \(\alpha+\beta\in\{-1,0,1\}\), \(0<| \alpha| ,| \beta| <1\). Mapping properties, boundedness and invertibility of such operators are studied in a scale of pairs of Besov type subspaces of \(C(-1,1)\).