Little Grothendieck's theorem for sublinear operators

An Interpolation Theorem for Sublinear Operators on 77„ Spaces

The purpose of this paper is to extend an interpolation theorem for sublinear operators on Lp spaces, obtained by Calderon and Zygmund, to similar operators acting on 77p spaces, p>0 [l]. We begin by making a few definitions. Let T be a mapping defined on a class of functions that are analytic in the interior of the unit circle \w\ <1, taking values that are measurable functions on some measure...

Frobenius kernel and Wedderburn's little theorem

We give a new proof of the well known Wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎We apply the concept of Frobenius kernel in Frobenius representation theorem in finite group‎ ‎theory to build a proof‎.

Triebel–Lizorkin space estimates for multilinear operators of sublinear operators

Let T be the singular integral operator, a well-known result of Coifman, Rochberg and Weiss [6] which states that the commutator [b,T ] = T (b f )− bT f (where b ∈ BMO) is bounded on Lp(Rn)(1 < p < ∞). Chanillo [1] proves a similar result when T is replaced by the fractional integral operator. In [9,11], these results on the Triebel–Lizorkin spaces and the case b∈Lipβ (where Lipβ is the homogen...

Cantor’s Little Theorem

This article discusses two theorems of Georg Cantor: Cantor’s Little Theorem and Cantor’s Diagonal Theorem.These results are obtained by generalizing the method of proof ofthe well known Cantor’s theorem about the cardinalities of a setand its power set. As an application of these, Gödel’s firstincompleteness theorem is proved. Hints are given as to how to derive other deeper results including ...

Fermat’s Little Theorem