Entire LP-functions of exponential type

We characterize the entire functions of exponential type, whose restriction to the real line is in L-P, in different ways: by the usual classical Paley Wiener growth estimates in the complex plane, by Bernstein inequalities using derivatives or differences, by L-P-growth properties of iterated derivatives or differences, and by support properties of the Fourier image. We also establish Paley Wiener theorems for the Fourier series of a function on the circle. (C) 2013 Elsevier GmbH. All rights reserved.