Properties of singular integral operators $S_{\alpha ,\beta }$

Amit Samanta, Santanu Sarkar

For $\alpha ,\beta \in L^{\infty }(S^1),$ the singular integral operator $S_{\alpha ,\beta }$ on $L^2(S^1)$ is defined by $S_{\alpha ,\beta }f:=\alpha Pf+\beta Qf$, where $P$ denotes the orthogonal projection of $L^2(S^1)…