Let $1 \lt q p \infty $, $1/r:=1/q-1/p$, and $T$ be a non-degenerate Calderón–Zygmund operator. We show that the commutator $[b,T]$ is compact from $L^p(\mathbb R^n)$ to $L^q(\mathbb if only $b=a+c$ with $a\in L^r(\mathbb $c

For two bound-state equations derived as simplified forms of the Bethe–Salpeter equation with confining interaction, stability of all solutions is rigorously shown. 1 Motivation: Instabilities of Klein-Paradox Type The Salpeter equation is a frequently applied three-dimensional reduction of the Bethe–Salpeter formalism describing bound states within quantum field theory, derived by assuming all...

The standard central limit theorem plays a fundamental role in Boltzmann-Gibbs statistical mechanics. This important physical theory has been generalized [1] in 1988 by using the entropy Sq = 1− P i p q i q−1 (with q ∈ R) instead of its particular BG case S1 = SBG = − P i pi ln pi. The theory which emerges is usually referred to as nonextensive statistical mechanics and recovers the standard th...