Some Remarks on Turán′s Inequality, II

Some remarks on weighted logarithmic Sobolev inequality

We give here a simple proof of weighted logarithmic Sobolev inequality, for example for Cauchy type measures, with optimal weight, sharpening results of BobkovLedoux [12]. Some consequences are also discussed.

Some remarks on Bell’s Inequality tests

We emphasize the difficulties of an experiment that can definitely discriminate between local realistic hidden variables theories and quantum mechanics using the Bell CHSH inequalities and a real measurement apparatus. In particular we analyze some examples in which the noise in real instruments can alter the experimental results, and the nontrivial problem to find a real “fair sample” of parti...

Some Remarks on the Fefferman-stein Inequality

We investigate the Fefferman-Stein inequality related a function f and the sharp maximal function f on a Banach function space X. It is proved that this inequality is equivalent to a certain boundedness property of the Hardy-Littlewood maximal operatorM . The latter property is shown to be self-improving. We apply our results in several directions. First, we show the existence of nontrivial spa...

Some remarks on the elliptic Harnack inequality

In this note we give three short results concerning the elliptic Harnack inequality (EHI), in the context of random walks on graphs. The first is that the EHI implies polynomial growth of the number of points in balls, and the second that the EHI is equivalent to an annulus type Harnack inequality for Green’s functions. The third result uses the lamplighter group to give a counterexample concer...

Some Remarks on Elementary Divisor Rings II