Intermediate Hankel operators on the Fock space

Let L2 = L2(D, r dr dθ/π) be the Lebesgue space on the open unit disc and let be the Bergman space. Let P be the orthogonal projection of L2 onto and let Q be the orthogonal projection onto . Then I − P ≥ Q. The big Hankel operator and the small Hankel operator on are defined as: for ϕ in L∞, and . In this paper, the finite‐rank intermediate Hankel operators between and are studied. We are working on the more general space, that is, the weighted Bergman space.

On Hankel operators associated with a class of non-Toeplitz operators

Some Nuclear Hankel Operators

We study Hankel operators on the weighted Fock spaces Fp γ. The boundedness and compactness of these operators are characterized in terms of BMO and VMO, respectively. Along the way, we also study Berezin transform and harmonic conjugates on the plane. Our results are analogous to Zhu’s characterization of bounded and compact Hankel operators on Bergman spaces of the unit disk.

Algebraic properties of small Hankel operators on the Fock space

In this paper we study boundedness of generalized Hankel operators of the form \documentclass{article}\usepackage{amssymb,mathrsfs}\begin{document}\pagestyle{empty}${\rm H}_{{\overline{z}}^k}^l: {\mathscr F}^2\big (|z|^2\big )\rightarrow L^2\big (|z|^2\big )$\end{document} and thereby extend our results from 10. Here, \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\rm H_{{\overline{z}}^k}^l(f):=(\rm Id-\rm P_l)\big (\overline{z}^k f\big )$\end{document} and Pl is the projection onto \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$A^2_l\big (\mathbb C,| z|^2\big ):=\rm cl\big (\rm span\lbrace \overline{z} ^mz^n\,|\,m,n\in \mathbb N,\,m\le l\rbrace \big )$\end{document}. Additionally, we extend our results to general conjugate‐holomorphic L2 symbols. The arguments applied show a tight connection between operator theory and combinatorics.