  We provide several Tauberian theorems for Laplace transforms with local
pseudofunction boundary behavior. Our results generalize and improve various
known versions of the Ingham-Fatou-Riesz theorem and the Wiener-Ikehara
theorem. Using local pseudofunction boundary behavior enables us to relax
boundary requirements to a minimum. Furthermore, we allow possible null sets of
boundary singularities and remove unnecessary uniformity conditions occurring
in earlier works; to this end, we obtain a useful characterization of local
pseudofunctions. Most of our results are proved under one-sided Tauberian
hypotheses; in this context, we also establish new boundedness theorems for
Laplace transforms with pseudomeasure boundary behavior. As an application, we
refine various results related to the Katznelson-Tzafriri theorem for power
series.
