Hankel operators on doubling Fock spaces

Suppose phi is a real-valued subharmonic function on C with Delta phi dA is a doubling measure. The doubling Fock space F phi pis the family of holomorphic functions on C such that f (center dot)e(-phi(<middle dot>)) is an element of L-p. We introduce the function space IDA(r)(s,q,alpha) and discuss the decomposition theorem for this space. We use it to characterize the boundedness and compactness of Hankel operators from a doubling Fock space F(phi)(p )to a weighted Lesbegue space L-phi(q) for all possible 1 <= p, q < infinity, which extends the results of [9] from the special case rho asymptotic to 1. We also obtain the relationship between the solution operators to partial derivative-equation and Hankel operator. As some applications, we obtain the characterizations on f for which Hankel operators H-f and H-f are both bounded (or compact) from F-phi(p) to L-phi(q).(c) 2023 Elsevier Inc. All rights reserved.