Weighted boundedness of multilinear integral operators for the endpoint cases

<abstract><p>We prove the weighted boundedness for the multilinear operators associated to some integral operators for the endpoint cases. The operators include Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.</p></abstract>

Pietsch’s variants of s-numbers for multilinear operators

We study variants of s-numbers in the context of multilinear operators. The notion of an $$s^{(k)}$$ s ( k ) -scale of k-linear operators is defined. In particular, we shall deal with multilinear variants of the $$s^{(k)}$$ s ( k ) -scales of the approximation, Gelfand, Hilbert, Kolmogorov and Weyl numbers. We investigate whether the fundamental properties of important s-numbers of linear operators are inherited to the multilinear case. We prove relationships among some $$s^{(k)}$$ s ( k ) -numbers of k-linear operators with their corresponding classical Pietsch’s s-numbers of a generalized Banach dual operator, from the Banach dual of the range space to the space of k-linear forms, on the product of the domain spaces of a given k-linear operator.

Weighted boundedness of multilinear pseudo-differential operators

<abstract><p>In this paper, the weighted boundedness for some multilinear operators generated by the pseudo-differential operators and the weighted Lipschitz functions are obtained.</p></abstract>

Domination and Kwapień’s factorization theorems for positive Cohen p–nuclear m–linear operators

In this paper, we introduce and study the concept of positive Cohen p-nuclear multilinear operators between Banach lattice spaces. We prove a natural analog to the Pietsch domination theorem for this class. Moreover, we give like the Kwapień’s factorization theorem. Finally, we investigate some relations with another known classes.

On the positive Dimant strongly $p$-summing multilinear operators

In 2003, Dimant V. has defined and studied the interesting class of strongly $p$-summing multilinear operators. In this paper, we introduce and study a new class of operators between two Banach lattices, where we extend the previous notion to the positive framework, and prove, among other results, the domination, inclusion and composition theorems. As consequences, we investigate some connections between our class and other classes of operators, such as duality and linearization.