Properties of singular integral operators Sα,β
Abstract
For α, β ∈ L∞ (S1), the singular integral operator Sα,β on L2 (S1) is defined by Sα,βf:= α Pf+β Qf, where P denotes the orthogonal projection of L2(S1) onto the Hardy space H2(S1), and Q denotes the orthogonal projection onto H2(S1). In a recent paper Nakazi and Yamamoto have studied the normality and self-adjointness of Sα,β. This work has shown that Sα,β may have analogous properties to that of the Toeplitz operator. In this paper we study several other properties of Sα,β.
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