Factorization of absolutely continuous polynomials

Abstract

Abstract. In this paper we study the ideal of dominated (p; σ)-continuous polynomials, that extend the nowadays well known ideal of p-dominated polynomials to the more general setting of the interpolated ideals of polynomials. We give the polynomial version of Pietsch's factorization Theorem for this new ideal. Although based in [11], our factorization theorem requires new techniques inspired in the theory of Banach lattices.

Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomials

“…This is the case of p-dominated homogeneous polynomials, for which a Pietsch type factorization theorem has been pursuit (see [28,31,9,14]) and succeeded just when the domain is separable. Related factorization schemes for homogeneous maps and polynomials can be found in [1] and [45]. Recently, the second and third authors [44] have isolated the class of p-dominated polynomials that satisfy a Pietsch type factorization theorem: the factorable p-dominated polynomials.…”