### The Extreme Points of a Class of Functions with Positive Real Part.

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Let 1 < p < ∞, q = p/(p-1) and for $f\in {L}^{p}(0,\infty )$ define $F\left(x\right)=(1/x){\u0283}_{0}^{x}f\left(t\right)dt$, x > 0. Moser’s Inequality states that there is a constant ${C}_{p}$ such that $su{p}_{a\le 1}su{p}_{f\in {B}_{p}}{\u0283}_{0}^{\infty}exp[a{x}^{q}{\left|F\left(x\right)\right|}^{q}-x]dx={C}_{p}$ where ${B}_{p}$ is the unit ball of ${L}^{p}$. Moreover, the value a = 1 is sharp. We observe that $F={K}_{1}$ f where the integral operator ${K}_{1}$ has a simple kernel K. We consider the question of for what kernels K(t,x), 0 ≤ t, x < ∞, this result can be extended, and proceed to discuss this when K is non-negative and homogeneous of degree -1. A sufficient condition on K is found for the analogue...

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