Abstract. As the classical (p, q)-Poincaré inequality is known to fail for 0 < p < 1, we introduce the notion of weighted multilinear Poincaré inequality as a natural alternative when m-fold products and 1/m < p are considered. We prove such weighted multilinear Poincaré inequalities in the subelliptic context associated to vector fields of Hörmader type. We do so by establishing multilinear re...

Nadirashvili presented a beautiful example showing that the Poincaré recurrence does not occur near a particular solution to the 2D Euler equation of inviscid incompressible fluids. Unfortunately, Nadirashvili’s setup of the phase space is not appropriate, and details of the proof are missing. This note fixes that.

Abstract In this paper, we unify and improve some of the results Bourgain, Brezis, Mironescu weighted Poincaré–Sobolev estimate by Fabes, Kenig, Serapioni. More precisely, get counterparts Poincaré–Sobolev-type inequality also Hardy type in fractional case under mild natural restrictions. A main feature obtain is fact that keep track behavior constants involved when parameter approaches to $1$....

Supersymmetry (SUSY), introduced in theoretical physics and mathematics, has a lot of interesting applications [1]. One of them consists in mixing fermionic and bosonic states. It has important consequences in the quantum field theory, namely, this property provides a mechanism for cancellation of the ultraviolet divergences. Moreover, supersymmetric quantum field theory (SSQT) allows to unify ...