Related papers: Weighted Weak-type Inequalities For Fractionally S…

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…

In this study, $(1,1)-$weak type boundedness of square function $S_{\alpha,\psi}$ is obtained by using Nazarov-Treil and Volberg technique. Also using this result, the $(1,1)-$ weak type boundedness of $g^{*}_{\lambda,\psi}$ operator is…

We analyze two weak random operators, initially motivated from processes in random environment. Intuitively speaking these operators are ill-defined, but using bilinear forms one can deal with them in a rigorous way. This point of view can…

In this paper we consider a generalized version of bounded oscillation operators, involving new parameters in the definition, as well as considering the operators on vector-valued function spaces. With this definition we will capture some…

In this work we extend Lacey's domination theorem to prove the pointwise control of bilinear Calder\'on--Zygmund operators with Dini--continuous kernel by sparse operators. The precise bounds are carefully tracked following the spirit in a…

Two proofs of a weighted weak-type $\left(1,\ldots,1;\frac{1}{m}\right)$ estimate for multilinear Calder\'on-Zygmund operators are given. The ideas are motivated by different proofs of the classical weak-type $(1,1)$ estimate for…

Due to its nonlocal nature, the $r$-variation norm Carleson operator $C_r$ does not yield to the sparse domination techniques of Lerner, Di Plinio and Lerner, Lacey. We overcome this difficulty and prove that the dual form to $C_r$ can be…

In this paper we prove the sharp boundedness for a fractional type operator given by a kernel that satisfy a $L^{\alpha,r'}$-H\"ormander conditions and a fractional size condition, where $0<\alpha<n$ and $1< r'\leq \infty$. To prove this…

In this paper, the weighted estimates for multilinear pseudo-differential operators were systematically studied in rearrangement invariant Banach and quasi-Banach spaces. These spaces contain the Lebesgue space, the classical Lorentz space…

In the context of variable exponent Lebesgue spaces equipped with a lower Ahlfors measure we obtain weighted norm inequalities over bounded domains for the centered fractional maximal function and the fractional integral operator.

We prove necessary and sufficient conditions for the weak-$L^p$ boundedness, for $p \in (1,\infty)$, of a maximal operator on the infinite-dimensional torus. In the endpoint case $p=1$ we obtain the same weak-type inequality enjoyed by the…

In this paper, we establish an operator-valued Fourier multiplier theorem in weighted Lebesgue spaces, Besov and Triebel--Lizorkin spaces, assuming the multiplier has $\mathcal{R}$-bounded range and satisfies an $\ell^r$-summability…

Assume $\mathcal{L}=-\Delta+V$ is a Schr\"{o}dinger operator on $\mathbb{R}^d$, where $V$ belongs to certain reverse H\"{o}lder class $RH_\sigma$ with $\sigma\geq d/2$. We consider the class of $A_{p,q}$ weights associated to $\mathcal{L}$,…

Let $T$ be a Fourier integral operator of order $-(n-1)/2$ associated with a canonical relation locally parametrised by a real-phase function. A fundamental result due to Seeger, Sogge, and Stein proved in the 90's, gives the boundedness of…

In this paper, we investigate the behavior of the bounds of the composition for rough singular integral operators on the weighted space. More precisely, we obtain the quantitative weighted bounds of the composite operator for two singular…

The aim of this article is to establish the $L^p(\mathbb{R}^2)$-boundedness of the variational operator associated with averaging operators defined over finite type curves in the plane. Additionally, we present the necessary conditions for…

In this paper, we give a sharp sparse domination of pseudodifferential operators associated with symbols belonging to the H\"{o}rmander class, and fundamental solutions of dispersive equations. Furthermore, we give boundedness results of…

In this paper, we show the strong and weak type boundedness of $T_{\Omega,\alpha}^A$ and $M_{\Omega,\alpha}^A$, the multilinear fractional integral operators and the corresponding fractional maximal operators, on the two weights weighted…

In this article, we introduce an analogue of Kenig and Stein's bilinear fractional integral operator on the Heisenberg group $\mathbb{H}^n$. We completely characterize exponents $\alpha, \beta$ and $\gamma$ such that the operator is bounded…

We introduce a class of operators on abstract measure spaces, which unifies the Calder\'on-Zygmund operators on spaces of homogeneous type, the maximal functions and the martingale transforms. We prove that such operators can be dominated…