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

Mathematische Annalen

### Criteria for Membership of Bloch Space and its Subspace, BMOA.

Mathematische Annalen

### Criteria for membership of the Besov spaces BS pq.

Mathematische Annalen

### Moser's Inequality for a class of integral operators

Studia Mathematica

Let 1 < p < ∞, q = p/(p-1) and for $f\in {L}^{p}\left(0,\infty \right)$ define $F\left(x\right)=\left(1/x\right){ʃ}_{0}^{x}f\left(t\right)dt$, x > 0. Moser’s Inequality states that there is a constant ${C}_{p}$ such that $su{p}_{a\le 1}su{p}_{f\in {B}_{p}}{ʃ}_{0}^{\infty }exp\left[a{x}^{q}{|F\left(x\right)|}^{q}-x\right]dx={C}_{p}$ 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...

### An inequality between compositions of weighted arithmetic and geometric means.

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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