The Norm of Certain Convolution Transforms on Lₚ Spaces of Entire Functions of Exponential Type

Denote by Bₚ (Ω ) the subspace of Lₚ ( - ∞ ,∞ ) whose elements are restrictions to the real line of entire functions of order l, type at most ω. It is shown that the norm of certain convolution transforms on Bₚ (Ω ) is independent of p, 1 ≤ p ≤ ∞. It follows that a number of classical inequalities sharp for functions in B_∞ (Ω ) are also sharp for functions in Bₚ (Ω ) with 1 ≤ p < ∞.