Zygmund’s inequality for entire functions of exponential type Original Research Article

Let f∈Lp(R)f∈Lp(R) be an entire function of exponential type σσ whose conjugate indicator diagram lies on interval View the MathML source[0,σi]. We prove that View the MathML source∫−∞∞|f′(x)|pdx≤cpσp∫−∞∞|Ref(x)|pdx(p≥1) Turn MathJax on where View the MathML sourcecp≔πΓ(1+p2)Γ(1+p2) is a best possible constant.