We study the following problem: Given a homogeneous polynomial from a sublattice of a Banach lattice to a Banach lattice, under which additional hypotheses does this polynomial factorize through -spaces involving multiplication operators? We prove that under some lattice convexity and concavity hypotheses, for polynomials certain vector-valued norm inequalities and weighted norm inequalities are equivalent. We combine these results and prove a factorization theorem for positive homogeneous polynomials which is a variant of a celebrated factorization theorem for linear operators due to Maurey and Rosenthal. Our main application is a Hahn-Banach extension theorem for positive homogeneous polynomials between Banach lattices.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm221-1-5,
author = {Andreas Defant and Mieczys\l aw Masty\l o},
title = {Factorization and extension of positive homogeneous polynomials},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {87-99},
zbl = {1303.47078},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm221-1-5}
}
Andreas Defant; Mieczysław Mastyło. Factorization and extension of positive homogeneous polynomials. Studia Mathematica, Tome 223 (2014) pp. 87-99. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm221-1-5/