Tusnády’s Inequality Revisited

Young’s Integral Inequality on Time Scales Revisited

A more complete Young’s integral inequality on arbitrary time scales (unbounded above) is presented.

The matrix arithmetic-geometric mean inequality revisited

The Sobolev Inequality on the Torus Revisited

We revisit the Sobolev inequality for periodic functions on the d-dimensional torus. We provide an elementary Fourier analytic proof of this inequality which highlights both the similarities and differences between the periodic setting and the classical ddimensional Euclidean one.

Grüss Type Discrete Inequalities in Inner Product Spaces, Revisited

Some sharp inequalities of Grüss type for sequences of vectors in real or complex inner product spaces are obtained. Applications for Jensen's inequality for convex functions defined on such spaces are also provided.

On Concentration and Revisited Large Deviations Analysis of Binary Hypothesis Testing

This paper first introduces a refined version of the Azuma-Hoeffding inequality for discrete-parameter martingales with uniformly bounded jumps. The refined inequality is used to revisit the large deviations analysis of binary hypothesis testing.