  Recently the authors characterized the Fredholmn properties of Toeplitz
operators on weighted Fock spaces when the Laplacian of the weight function is
bounded below and above. In the present work the authors extend their
characterization to doubling Fock spaces with a subharmonic weight whose
Laplacian is a doubling measure. The geometry induced by the Bergman metric for
doubling Fock spaces is much more complicated than that of the Euclidean metric
used in all the previous cases to study Fredholmness, which leads to
considerably more involved calculations.
