Related papers: Sparse domination implies vector-valued sparse dom…

We obtain boundedness from a product of Lebesgue or Hardy spaces into Hardy spaces under suitable cancellation conditions for a large class of multilinear operators that includes the Coifman-Meyer class, sums of products of linear…

The Hardy-Littlewood maximal operator satisfies the classical Sawyer-type estimate $$ \left \Vert \frac{Mf}{v}\right \Vert_{L^{1,\infty}(uv)} \leq C_{u,v} \Vert f \Vert_{L^{1}(u)}, $$ where $u\in A_1$ and $uv\in A_{\infty}$. We prove a…

A proof is given for the "only if" part of the result stated in the previous paper of the series that a suitably nondegenerate Calder\'on-Zygmund operator $T$ is bounded in a Banach lattice $X$ on $\mathbb R^n$ if and only if the…

Let $\nu = (\nu_1, \ldots, \nu_n) \in (-1/2, \infty)^n$, with $n \ge 1$, and let $\Delta_\nu$ be the multivariate Bessel operator defined by \[ \Delta_{\nu} = -\sum_{j=1}^n\left( \frac{\partial^2}{\partial x_j^2} - \frac{\nu_j^2 -…

Let a vector-valued sublinear operator satisfy the size condition and be bounded on weighted Lebesgue spaces with variable exponent. Then we obtain its boundedness on weighted grand Herz-Morrey spaces with variable exponents. Next we…

Building on the notion of convex body domination introduced by Nazarov, Petermichl, Treil, and Volberg, we provide a general principle of bootstrapping bilinear estimates for scalar-valued functions into vector-valued versions with a…

Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$ satisfying some mild assumptions. In this article, the authors first find a reasonable version $\widetilde{T}$ of the Calder\'on--Zygmund operator $T$ on the ball…

We extend the recently much-studied Hardy factorization theorems to the weight case. The key point of this paper is to establish the factorization theorems without individual condition on the weight functions. As a direct application, we…

This paper is devoted to studying the Rubio de Francia extrapolation for multilinear compact operators. It allows one to extrapolate the compactness of $T$ from just one space to the full range of weighted spaces, whenever an $m$-linear…

We represent a general bilinear Calder\'on-Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so called sparse T1…

We consider a class of (ill-posed) optimal control problems in which a distributed vector-valued control is enforced to pointwise take values in a finite set $\mathcal{M}\subset\mathbb{R}^m$. After convex relaxation, one obtains a…

We consider the fractional derivative of a general Poisson semigroup. With this fractional derivative we define the generalized fractional Littlewood-Paley $g$-function for semigroups acting on $L^p$-spaces of functions with values in…

A complex number $\lambda$ is called an extended eigenvalue of a bounded linear operator $T$ on a Banach space $\B$ if there exists a non-zero bounded linear operator $X$ acting on $\B$ such that $XT=\lambda TX$. We show that there are…

Let $2\leq p<\infty$ and $X$ be a complex infinite-dimensional Banach space. It is proved that if $X$ is $p$-uniformly PL-convex, then there is no nontrivial bounded Volterra operator from the weak Hardy space…

We prove $L^p$-bounds for the bilinear Hilbert transform acting on functions valued in intermediate UMD spaces. Such bounds were previously unknown for UMD spaces that are not Banach lattices. Our proof relies on bounds on embeddings from…

The multilinear pseudo-differential operators with symbols in the multilinear H\"ormander class $S_{0,0}$ are considered. A complete identification of the cases where those operators define bounded operators between local Hardy spaces is…

In this paper, the sharp maximal theorem is generalized to mixed-norm ball Banach function spaces, which is defined as Definition 2.7. As an application, we give a characterization of BMO via the boundedness of commutators of fractional…

We prove sparse bounds for pseudodifferential operators associated to H\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of weighted estimates…

We introduce and study the class of positive weakly (q,r)-dominated multilinear operators between Banach lattices. This notion extends classical domination and summability concepts to the positive multilinear setting and generates a new…

In the present work, we find useful and explicit necessary and sufficient conditions for linear and multilinear multiplier operators of Coifman-Meyer type, finite sum of products of Calder\'on-Zygmund operators, and also of intermediate…