Related papers: A note on multiple summing operators and applicati…
In the last decades many authors have become interested in the study of multilinear and polynomial generalizations of families of operator ideals (such as, for instance, the ideal of absolutely summing operators). However, these…
We present an extension of the Hardy--Littlewood inequality for multilinear forms. More precisely, let $\mathbb{K}$ be the real or complex scalar field and $m,k$ be positive integers with $m\geq k\,$ and $n_{1},\dots ,n_{k}$ be positive…
We consider estimates of Hardy and Littlewood for norms of operators on sequence spaces, and we apply a factorization result of Maurey to obtain improved estimates and simplified proofs for the special case of a positive operator.
In recent years, there has been a lot of progress in obtaining non-trivial bounds for bilinear forms of Kloosterman sums in $\mathbb{Z}/m\mathbb{Z}$ for arbitrary integers $m$. These results have been motivated by a wide variety of…
This short note has a twofold purpose: (i) to solve the question that motivates a recent paper of D. Popa on multilinear variants of Pietsch's composition theorem for absolutely summing operators. More precisely, we remark that there is a…
With rectangular doubling weight, a~generalized Hardy-Littlewood-Sobolev inequality for rectangular fractional integral operators is verified. The result is a~nice application of $M$-linear embedding theorem for dyadic rectangles.
We apply the geometric approach provided by $\Sigma$-operators to develop a theory of $p$-summability for multilinear operators. In this way, we introduce the notion of Lipschitz $p$-summing multilinear operators and show that it is…
In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let $\vec{w}=(w_1,...,w_m)$ and $\nu = w_1^\frac{1}{m}...w_m^\frac{1}{m}$, the main result of the…
In this paper we provide an abstract aproach to the study of classes of multiple summing multilinear operators between Banach spaces. The main purpose is unify the study of several known classes and results, for example multiple $(p,…
We present new bounds for the Berezin number inequalities which improve on the existing bounds. We also obtain bounds for the Berezin norm of operators as well as the sum of two operators.
We prove several singular value inequalities for sum and product of compact operators in Hilbert space. Some of our results generalize the previous inequalities for operators. Also, applications of some inequalities are given.
In this note, some refinements of Young inequality and its reverse for positive numbers are proved and using these inequalities some operator versions and Hilbert-Schmidt norm versions for matrices of these inequalities are obtained.
The multilinear Hardy--Littlewood inequalities provide estimates for the sum of the coefficients of multilinear forms $T:\ell_{p_{1}}^{n}\times\cdots \times\ell_{p_{m}}^{n}\rightarrow\mathbb{R}$ (or $\mathbb{C}$) when…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…
We study an inequality suggested by Littlewood, our result refines a result of Bennett.
In this short note we give counterexamples to several results related to extension theorems published recently.
We investigate lineability/spaceability problems within the setting of multilinear summing operators on quasi-Banach sequence spaces. Furthermore, we deal with the contemporary geometric notions of pointwise-lineability and…
The addition relation for the Riemann theta functions and for its limits, which lead to the appearance of exponential functions in soliton type equations is discussed. The presented form of addition property resolves itself to the…
We obtain all extreme and exposed points of the closed unit ball of the space of bilinear forms $T:\ell_{\infty}^{2}\times\ell_{\infty}^{2}\rightarrow \mathbb{R}.$ We also show that any (norm one) bilinear form $T:\ell_{\infty…
The goal of this note is to prove a analogue of the Littewood-Paley decomposition for densities of operators and to use it in the context of Lieb-Thirring inequalities.