Slant Toeplitz operators on the Bergman space

Abstract In this paper, we establish a necessary and sufficient condition for a bounded linear operator on the Bergman space to be a slant Toeplitz operator having an analytic symbol. Moreover, we obtain a complete characterization for the commutativity of two slant Toeplitz operators with symbols <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mover accent="true"> <m:mi>p</m:mi> <m:mo>¯</m:mo> </m:mover> <m:mo>+</m:mo> <m:mi>φ</m:mi> </m:mrow> </m:math> {\overline{p}+\varphi} and ψ on the Bergman space, where φ and ψ are two bounded analytic functions, and p is an analytic polynomial.