Related papers: Multilinear estimates for Calder\'on commutators

In this paper, we investigate the weighted multilinear boundedness properties of the maximal higher order Calder\'on commutator for the dimensions larger than two. We establish all weighted multilinear estimates on the product of the…

In this paper, we establish some bilinear endpoint estimates of Calder\'on commutator $\mathcal{C}[\nabla A,f](x)$ with a homogeneous kernel when $\Omega\in L\log^+L(\mathbf{S}^{d-1})$. More precisely, we prove that $\mathcal{C}[\nabla…

In this paper, we consider the boundedness properties of multilinear $\theta$-type Calder\'on--Zygmund operators $T_\theta$ recently introduced in the literature. First, we prove strong type and weak type estimates for multilinear…

In this paper, the authors establish some weighted estimates for the Calder\'on commutator defined by \begin{eqnarray*} &&\mathcal{C}_{m+1,\,A}(a_1,\dots,a_{m};f)(x) &&\quad={\rm…

In this work we fully characterize the classes of matrix weights for which multilinear Calder\'on-Zygmund operators extend to bounded operators on matrix weighted Lebesgue spaces. To this end, we develop the theory of multilinear singular…

Iterated commutators of multilinear Calderon-Zygmund operators and pointwise multiplication with functions in $BMO$ are studied in products of Lebesgue spaces. Both strong type and weak end-point estimates are obtained, including weighted…

Let $T_{\vec{b}}$ and $T_{\Pi b}$ be the commutators in the $j$-th entry and iterated commutators of the multilinear Calder\'{o}n-Zygmund operators, respectively. It was well-known that $T_{\vec{b}}$ and $T_{\Pi b}$ were not of weak type…

In this paper, the sharp quantitative weighted bounds for the iterated commutators of a class of multilinear operators were systematically studied. This class of operators contains multilinear Calder\'{o}n-Zygmund operators, multilinear…

We prove $L^p$ bounds for the extensions of standard multilinear Calder\'on-Zygmund operators to tuples of UMD spaces tied by a natural product structure. This can, for instance, mean the pointwise product in UMD function lattices, or the…

We show that the product BMO space can be characterized by iterated commutators of a large class of Calder\'on-Zygmund operators. This result follows from a new proof of boundedness of iterated commutators in terms of the BMO norm of their…

We deal with the boundedness properties of higher order commutators related to some generalizations of the multilinear fractional integral operator of order $m$, $I_\alpha ^m$, from a product of weighted Lebesgue spaces into adequate…

We develop a wide general theory of bilinear bi-parameter singular integrals $T$. First, we prove a dyadic representation theorem starting from $T1$ assumptions and apply it to show many estimates, including $L^p \times L^q \to L^r$…

In this paper, we develop a comprehensive weighted theory for a class of Banach-valued multilinear bounded oscillation operators on measure spaces, which merges multilinear Calder\'{o}n-Zygmund operators with a quantity of operators beyond…

For a general dyadic grid, we give a Calder\'{o}n-Zygmund type decomposition, which is the principle fact about the multilinear maximal function $\mathfrak{M}$ on the upper half-spaces. Using the decomposition, we study the boundedness of…

In this paper, the author studies the boundedness for a large class of sublinear operator $T_\alpha, \alpha\in[0,n)$ generated by Calder{\'o}n-Zygmund operators ($\alpha=0$) and generated by fractional integral operator ($\alpha>0$) on…

In this article, we address pointwise sparse domination for multilinear Calder\'on-Zygmund operators on upper doubling, geometrically doubling metric measure spaces. As a consequence, we have obtained sharp quantitative weighted estimates…

In this paper, we study the boundedness for a large class of multi-sublinear operators $T_m$ generated by multilinear Calder{\'o}n-Zygmund operators and their commutators $T^{b}_{m,i}~(i=1,\cdots,m)$ on the product generalized mixed Morrey…

We establish Calder\'on-type theorems for operators bounded on nonstandard end-point Lorentz spaces \begin{equation*} T\colon L^{p_0, q_0}\to L^{p_1, q_1}\quad\text{and}\quad T\colon L^{q, 1}\to L^\infty \end{equation*} and the improvement…

Let $T$ be a multilinear Calder\'on-Zygmund operator of type $\omega$ with $\omega(t)$ being nondecreasing and satisfying a kind of Dini's type condition. Let $T_{\Pi\vec{b}}$ be the iterated commutators of $T$ with $BMO$ functions. The…

We prove Bloom type two-weight inequalities for commutators of multilinear singular integral operators including Calder\'on-Zygmund operators and their dyadic counterparts. Such estimates are further extended to a general higher order…