Bounded and Compact Toeplitz Operators with Positive Measure Symbol on Fock-Type Spaces

Abstract

In this note, we discuss the Bergman projection P and Toeplitz operators $$T_{\mu }$$ with positive measure symbol $$\mu $$ between $$F^p_{\Psi }(\mathbb {C}^n)$$ and $$F^q_{\Psi }(\mathbb {C}^n)$$ for $$1\le p, q\le \infty $$ . We first show that P is a bounded projection from $$L^p_{\Psi }$$ onto $$F^p_{\Psi }$$ when $$1\le p\le \infty $$ , and then apply it to obtain results on the complex interpolation and the duality of the Fock-type spaces. Furthermore, we obtain the equivalent conditions for the boundedness and compactness of $$T_{\mu }$$ in terms of the averaging function and the Berezin transform, which extend the main results about Toeplitz operators of Seip and Youssfi (J Geom Anal 23:170–201, 2013).