Properties of singular integral operators $S_{α,β}$

Amit Samanta; Santanu Sarkar

paper

Properties of singular integral operators $S_{α, β}$

arXiv:1505.05326

Abstract

For $α, β \in L^{\infty} (S^{1}),$ the singular integral operator $S_{α, β}$ on $L^{2} (S^{1})$ is defined by $S_{α, β} f := α P f + β Q f$ , where $P$ denotes the orthogonal projection of $L^{2} (S^{1})$ onto the Hardy space $H^{2} (S^{1}),$ and $Q$ denotes the orthogonal projection onto $H^{2} (S^{1})^{⊥} .$ In a recent paper Nakazi and Yamamoto have studied the normality and self-adjointness of $S_{α, β} .$ This work has shown that $S_{α, β}$ may have analogous properties to that of the Toeplitz operator. In this paper we study several other properties of $S_{α, β} .$

19 pages

Properties of singular integral operators Sα,β​

Abstract

Properties of singular integral operators $S_{α, β}$