Related papers: Weighted Bilinear Multiplier Theorems in Dunkl Set…
Let $T$ be a multilinear integral operator which is bounded on certain products of Lebesgue spaces on $\mathbb R^n$. We assume that its associated kernel satisfies some mild regularity condition which is weaker than the usual H\"older…
In this paper, we prove the boundedness of the multilinear Littlewood-Paley square operators and their commutators on weighted Morrey spaces, then we give the boundedness and weak-type $L\log L$ estimates for the commutators of multilinear…
We develop a general theory of multilinear singular integrals with operator-valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the $\mathcal R$-boundedness condition…
The recent proof of the sharp weighted bound for Calder\'on-Zygmund operators has led to much investigation in sharp mixed bounds for operators and commutators, that is, a sharp weighted bound that is a product of at least two different…
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…
In \cite{MR447956}, Muckenhoupt and Wheeden formulated a weighted weak $(p,p)$ inequality where the weight for the weak $L^p$ space is treated as a multiplier rather than a measure. They proved such inequalities for the Hardy-Littlewood…
In recent work by Reguera and Thiele and by Reguera and Scurry, two conjectures about joint weighted estimates for Calder\'on-Zygmund operators and the Hardy-Littlewood maximal function have been refuted in the one-dimensional case. One of…
In this paper we develop a kind of A_p theory for Calderon-Zygmund operators in a non-homogeneous setting. Let \mu be a Borel measure on \R^d which may be non doubling. The only condition that \mu must satisfy is \mu(B(x,r))\leq Cr^n for…
In this paper, we investigate the boundedness of bilinear Calder\'on-Zygmund operators $T$ from ${L^{p_1}\left(w_1\right)} \times {L^{p_2}\left(w_2\right)}$ to ${L^{p,\infty}\left(v_{\vec{w}}\right)}$ with the stopping time method, where $1…
We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calder\'on-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by Sawyer estimating…
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 obtain the off-diagonal Muckenhoupt-Wheeden conjecture for Calder\'on-Zygmund operators. Namely, given $1<p<q<\infty$ and a pair of weights $(u,v)$, if the Hardy-Littlewood maximal function satisfies the following two weight…
Motivated by the study of kernels of bilinear pseudodifferential operators with symbols in a H\"ormander class of critical order, we investigate boundedness properties of strongly singular Calder\'on--Zygmund operators in the bilinear…
In this paper, weighted norm inequalities with $A_p$ weights are established for the multilinear singular integral operators whose kernels satisfy $L^{r'}$-H\"ormander regularity condition. As applications, we recover a weighted estimate…
In this article, we investigate the unweighted and weighted $L^p$-boundedness of pseudo-multipliers associated with a class of Schr\"odinger operators. The weight classes we consider are tailored to this framework and strictly contain the…
In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we discuss the strong type and weak type estimates for a class of Calder\'on--Zygmund type operators $T_\theta$ in these new weighted spaces. Furthermore, the…
We consider several harmonic analysis operators in the multi-dimensional context of the Dunkl Laplacian with the underlying group of reflections isomorphic to $\mathbb{Z}_2^n$ (also negative values of the multiplicity function are…
We study optimal multiple weight assumptions in the weighted theory of multilinear Fourier multipliers and multilinear pseudo-differential operators. For multilinear Fourier multipliers, we revisit the weighted H\"ormander-type theorem of…
In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function $\Mm$ introduced in \cite{LOPTT} and for multilinear Calder\'on-Zygmund operators. In particular we obtain a sharp mixed…
In this paper we solve a long standing problem about the bilinear $T1$ theorem to characterize the (weighted) compactness of bilinear Calder\'{o}n-Zygmund operators. Let $T$ be a bilinear operator associated with a standard bilinear…