On the sublinear operators factoring throughLq

ON THE SUBLINEAR OPERATORS FACTORING THROUGH Lq LAHCÈNE MEZRAG and ABDELMOUMENE TIAIBA

Let 0 < p ≤ q ≤ +∞. Let T be a bounded sublinear operator from a Banach space X into an Lp(Ω,μ) and let ∇T be the set of all linear operators ≤ T . In the present paper, we will show the following. Let C be a positive constant. For all u in ∇T , Cpq(u) ≤ C (i.e., u admits a factorization of the form X ũ → Lq(Ω,μ) Mgu → Lp(Ω,μ), where ũ is a bounded linear operator with ‖ũ‖ ≤ C , Mgu is the bo...

Boundedness of Sublinear Operators on the Homogeneous Herz Spaces

Uniformly Factoring Weakly Compact Operators

Let X and Y be separable Banach spaces. Suppose Y either has a shrinking basis or Y is isomorphic to C(2N) andA is a subset of weakly compact operators from X to Y which is analytic in the strong operator topology. We prove that there is a reflexive space with a basis Z such that every T ∈ A factors through Z. Likewise, we prove that if A ⊂ L(X,C(2N)) is a set of operators whose adjoints have s...

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...

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...