Hankel operators on doubling Fock spaces (Q6542836)

Let \(\Delta\) be the Laplace operator and \(\phi:\mathbb{C}\to\mathbb{R}\), \(dA\) be the area measure on\(\mathbb{C}\), and \(\phi:\mathbb{C}\to\mathbb{R}\) be a subharmonic function function such that \(\Delta\phi dA\) is a doubling measure on \(\mathbb{C}\). For \(1\le p<\infty\), the space \(L_\phi^p\) consists of all measurable functions \(f:\mathbb{C}\to\mathbb{C}\) such that \(\int_\mathbb{C} |f(z)e^{-\phi(z)}|^p dA(z)<\infty\). The doubling Fock space is defined by \(F_\phi^p=L_\phi^p\cap H(\mathbb{C})\), where \(H(\mathbb{C})\) is the family of entire functions. The authors found necessary and sufficient conditions for the boundedness and compactness of the big Hankel operator \(H_f:F_\phi^p\to L_\phi^q\) and the pair of big Hankel operators \(H_f,H_{\overline{f}}:F_\phi^p\to L_\phi^q\) for all possible \(1\le p\le q<\infty\).