Bergman spaces on the complement of a lattice

摘要

We investigate Bergman spaces B p (Ω), where Ω = C(Z + i Z) and show that B p = {0} for p ≥ 2 and {0} ≠ B q $subset$ B p for 2/(n + 1) ≤ q < p < 2. Further, for each 0 < p < 2 there is a non-trivial $f in B^p$ tending to zero at infinity at any prescribed rate. We also give conditions on the Mittag-Leffler expansion of f necessary for $f in B^p$.