Let H(S) be the Hardy space on the unit sphere S in C. We establish a local inequality for Hankel operators Hf = (1 − P )Mf |H(S). As an application of this local inequality, we characterize the membership of Hf in the Lorentz-like ideal C p , 2n < p <∞.

1 We study relationships between Logarithmic Sobolev inequalities with one parameter of Davies-Simon type, energy-entropy inequality, Nash-type inequality and Sobolev-type inequalities. The inequalities of Sobolev-type apply in the general setting of symmetric sub-Markovian semigroups (and some generalizations). We provide several examples of application of theses results for ultracontractive s...

It is nowadays well-known that Hardy’s inequality (like many other inequalities) follows directly from Jensen’s inequality. Most of the development of Hardy type inequalities has not used this simple fact, which obviously was unknown by Hardy himself and many others. Here we report on some results obtained in this way mostly after 2002 by mainly using this fundamental idea.

We present a refinement of a known entropic inequality on the sphere, finding suitable conditions underwhich the uniformprobabilitymeasure on the sphere behaves asymptomatically like the Gaussian measure on R N with respect to the entropy. Additionally, we remark about the connection between this inequality and a the investigation of themany body Cercignani’s conjecture.

We give a new proof of a recent inequality for bicentric quadrilaterals that is an extension of the Euler-like inequality R ≥ √ 2r. A bicentric quadrilateral ABCD is a convex quadrilateral that has both an incircle and a circumcircle. In [6], Zhang Yun called these “double circle quadrilaterals” and proved that

Metric spaces provide a framework for analysis and have several very useful properties. Many of these properties follow in part from the triangle inequality. However, there are several applications in which the triangle inequality does not hold but in which we may still like to perform analysis. This paper investigates what happens if the triangle inequality is removed all together, leaving wha...

This paper constructs a simple theoretical model to study the implications of globalization for inequality and redistribution. It shows that when globalization increases inequality, a policymaker interested in maximizing the sum of welfares of all agents increases redistribution. Empirically, the paper examines the e¤ects of globalization on inequality and redistribution in a panel data set of ...