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We present an extension of the Hardy-Littlewood inequality for multi-linear forms. This extension combines repetitions of indexes in the summands and perturbation of the exponent. In particular, we recover a recent result due to G. Araujo and D. Pellegrino. [ABSTRACT FROM AUTHOR]

It is well known that not every summability property for multilinear operators leads to a factorization theorem. In this paper we undertake a detailed study of factorization schemes for summing linear and nonlinear operators. Our aim is to integrate under the same theory a wide family of classes of mappings for which a Pietsch type factorization theorem holds. Our construction includes the cases of absolutelyp-summing linear operators, (p, σ)-absolutely continuous linear operators, factorable stronglyp-summing multilinear operators, (p1, . . . , pn)-dominated multilinear operators and dominated (p1, . . . , pn;σ)-continuous multilinear operators. [ABSTRACT FROM PUBLISHER]

Letbe the canonical map, whereis a regular Borel probability measure on the closed unit ballof the dualof a Banach spaceendowed with the weak* topology. This paper has a twofold purpose: (i) to study when-summing linear operators/-dominated homogeneous polynomials onhave a Pietsch measure for which the canonical map is injective; (ii) to show how these results can be used to correct the proofs of some results of the authors concerning Pietsch-type factorization of dominated polynomials. [ABSTRACT FROM PUBLISHER]