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1 Studia Mathematica

1 2014

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Factorization and extension of positive homogeneous polynomials

100%

Defant A. , Mastyło M.

nr 1

87-99

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 $L_{p}$-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.