Entire Functions of Exponential Type Belonging to L p (R)

We prove for entire functions of exponential type an inequality which is analogous to a classical inequality of J. Marcinkiewicz. Our inequality can just as well be seen as an extension of a result of M. Plancherel and G. Pólya. In passing, we obtain a generalized version of the famous Whittaker‐Shannon Sampling Theorem.