Related papers: Absolutely summing multilinear operators on $\ell_…

We prove a new result on multiple summing operators and among other applications, we provide a new extension of Littlewood's $4/3$ inequality to $m$-linear forms.

In this paper, for $p> 1 $ and $r \ge 1$ we provide a complete characterization of the positive Borel measures $\mu$ on the unit ball $\B_n$ of $\mathbb {C}^n$ for which the induced Toeplitz operator $T_\mu$ is $r$-summing on the Bergman…

We continue our study of the mapping ideal of operator $p$-compact maps, previously introduced by the authors. Our approach embraces a more geometric perspective, delving into the interplay between operator $p$-compact mappings and matrix…

We give a new proof of a characterization of the closeness of the range of a continuous linear operator and of the closeness of the sum of two closed vector subspaces of a Banach space. Then we state sufficient conditions for the closeness…

Let $1\le p\le q<\infty$ and let $X$ be a $p$-convex Banach function space over a $\sigma$-finite measure $\mu$. We combine the structure of the spaces $L^p(\mu)$ and $L^q(\xi)$ for constructing the new space $S_{X_p}^{\,q}(\xi)$, where…

We prove bounds for multilinear operators on $\R^d$ given by multipliers which are singular along a $k$ dimensional subspace. The new case of interest is when the rank $k/d$ is not an integer. Connections with the concept of {\em true…

For a separable rearrangement invariant space $X$ on $(0,\infty)$ of fundamental type we identify the set of all $p\in [1,\infty]$ such that $\ell^p$ is finitely represented in $X$ in such a way that the unit basis vectors of $\ell^p$…

As is well known absolute convergence and unconditional convergence for series are equivalent only in finite dimensional Banach spaces. Replacing the classical notion of absolutely summing operators by the notion of 1 summing operators \[…

In this note we prove a general version of the Extrapolation Theorem, extending the classical linear extrapolation theorem due to B. Maurey. Our result shows, in particular, that the operators involved do not need to be linear.

In a recent survey paper we introduced one-sided multipliers between two different operator spaces. Here we give some basic theory for these maps.

We discuss the multiple summability of a multilinear map $T:X_1\times\cdots\times X_m\to Y$ when we have informations on the summability of the maps it induces on each coordinate. Our methods have applications to inclusion theorems for…

We establish $L^{p_1}\times\cdots\times L^{p_k}\to L^r$ and $\ell^{p_1}\times\cdots\times \ell^{p_k}\to \ell^r$ type bounds for multilinear maximal operators associated to averages over isometric copies of a given non-degenerate $k$-simplex…

Let $A,B\in B(H)$. In the present paper, we establish simple and interesting facts on when we have $|A||B|=|B||A|$, $|AB|=|A||B|$, $|A\pm B|\leq |A|+|B|$, $||A|-|B||\leq |A\pm B|$ and $\||A|-|B|\|\leq \|A\pm B\|$, where $|\cdot|$ denotes…

We prove L^p estimates for a large class of multi-linear operators, which includes the multi-linear paraproducts studied by Coifman and Meyer, as well as the bilinear Hilbert transform.

For $f \in H^p(\delta^2)$, $0<p\leq 2$, with Haar expansion $f=\sum f_{I \times J}h_{I\times J}$ we constructively determine the Pietsch measure of the $2$-summing multiplication operator \[\mathcal{M}_f:\ell^{\infty} \rightarrow…

Via the new weight $A_{\vec p}^{\theta }(\varphi )$, the authors introduce a new class of multilinear square operators. The boundedness on the weighted Lebesgue space and the weighted Morrey space is obtained, respectively. Our results…

We investigate possible quantifications of strictly singular operators, $l_{p}$-strictly singular operators, $c_{0}$-strictly singular operators, strictly cosingular operators, $l_{p}$-strictly cosingular operators. We prove quantitative,…

Representations of polynomial covariant type commutation relations by pairs of linear integral operators and multiplication operators on Banach spaces $L_p$ are constructed.

In this note we give a characterization of $\ell^{p}\times ...\times \ell^{p}\to\ell^q$ boundedness of maximal operators associated to multilinear convolution averages over spheres in $\mathbb{Z}^n$.

We characterize those bounded multilinear operators that factor through a Hilbert space in terms of its behavior in finite sequences. This extends a result, essentially due to S. Kwapie\'{n}, from the linear to the multilinear setting. We…