On the sublinear operators factoring through L q

Lahcène Mezrag and Abdelmoumene Tiaiba

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-10

Abstract:

Let 0 < p ≤ q ≤ + ∞ . Let T be a bounded sublinear operator from a Banach space X into an L p ( 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 , C p q ( u ) ≤ C (i.e., u admits a factorization of the form X → u ˜ L q ( Ω , μ ) → M g u L q ( Ω , μ ) , where u ˜ is a bounded linear operator with ‖ u ˜ ‖ ≤ C , M g u is the bounded operator of multiplication by g u which is in B L r + ( Ω , μ ) ( 1 / p = 1 / q + 1 / r ), u = M g u ∘ u ˜ and C p q ( u ) is the constant of q -convexity of u ) if and only if T admits the same factorization; This is under the supposition that { g u } u ∈ ∇ T is latticially bounded. Without this condition this equivalence is not true in general.

Date: 2004
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2004/961791.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2004/961791.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:961791

DOI: 10.1155/S0161171204303145

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().