Toeplitz operators on Bergman spaces with exponential weights for 0 < p ≤ 1

Given 0 < p < infinity, the Bergman space A(phi)(p) consists of all holomorphic functions on D such that parallel to integral parallel to(p,phi) = (integral(D)vertical bar integral(z)e(-phi(z))vertical bar(p) dA(z))(1/p) < infinity, where phi belongs to a large class W-0 which cover those defined by Borichev, Dhuez and Kellay (2007) [4]. For 0 < p < 1, A(phi)(p) is neither a self-adjoint nor Banach space. By new approaches, we study the characterizations on positive Borel measures mu on D for which the induced Toeplitz operators T-mu are bounded or compact from one Bergman space A(phi)(p) to another A(phi)(q) for p or q is an element of (0, 1]. (C) 2021 Published by Elsevier Masson SAS.