Related papers: Weighted weak type $(1,1)$ estimates for oscillato…

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…

In this paper, we show that $W^{1,p}$ $(1\leq p<\infty)$ weak solutions to divergence form elliptic systems are Lipschitz and piecewise $C^{1}$ provided that the leading coefficients and data are of piecewise Dini mean oscillation, the…

In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n-1})$ and the Bochner-Riesz multiplier at the critical index $B_{(n-1)/2}$.…

In this work we provide a criterion for the global weak (1,1) type of integral operators which are known to be locally uniformly of weak (1,1) type. As an application, we establish the global weak (1,1) type for a class of Fourier integral…

We prove weighted estimates for singular integral operators which operate on function spaces on a half-line. The class of admissible weights includes Muckenhoupt weights and weights satisfying Sawyer's one-sided conditions. The kernels of…

Let $T_a$ be a pseudo-differential operator defined by exotic symbol $a$ in H\"{o}rmander class $S^m_{0,\delta}$ with $m \in \mathbb{R} $ and $0 \leq \delta \leq 1 $. It is well-known that the weak type (1,1) behavior of $T_a $ is not fully…

In 2006, Janakiraman [10] showed that if $\Omega$ with mean value zero on $S^{n-1}$ satisfies the condition \[ \sup_{|\xi|=1}\int_{S^{n-1}}|\Omega(\theta)-\Omega(\theta+\delta\xi)|d\sigma(\theta)\leq…

Given a bilinear (or sub-bilinear) operator $B$, we prove restricted weighted weak type inequalities of the form $$ ||B(f_1, f_2)||_{L^{p, \infty}(w_1^{p/p_1}w_2^{p/p_2})}\lesssim ||f_1||_{L^{p_1, 1}(w_1)}||f_2||_{L^{p_2, 1}(w_2)}, $$…

In this paper, we study the quantitative weighted bounds for the $q$-variational singular integral operators with rough kernels. The main result is for the sharp truncated singular integrals itself $$…

In this paper, we investigate the weighted vector-valued bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};\,\mathbb{R}^n,w_1)\times\dots\times L^{p_m}(l^{q_m};\,\mathbb{R}^n,w_m)$ to…

We prove sharp weak type weighted estimates for a class of sparse operators that includes majorants of standard $\alpha$-fractional singular integrals, fractional integral operators, Marcinkiewicz integral operators, and square functions.…

Let $0\leq \alpha<n$, $m\in \mathbb{N}$ and let consider $T_{\alpha,m}$ be a of integral operator, given by kernel of the form $$K(x,y)=k_1(x-A_1y)k_2(x-A_2y)\dots k_m(x-A_my),$$ where $A_i$ are invertible matrices and each $k_i$ satisfies…

In this paper we study Coifman type estimates and weighted norm inequalities for singular integral operators $T$ and its commutators, given by the convolution with a vector valued kernel $K$. We define a weaker H\"ormander type condition…

We establish weighted norm inequalities for multilinear singular integral operators with rough kernels. Specifically, we consider the multilinear singular integral operator $\mathcal{L}_\Omega$ associated with an integrable function…

We establish H\"older and Harnack estimates for weak solutions of a class of elliptic nonlocal equations that are modeled on integro-differential operators with kernels of measure. The approach is of De Giorgi-type, as developed by…

In this paper it is shown that for $\Omega\in L\log L(\mathbb{S}^{d-1})$, the rough maximal singular integral operator $T_\Omega^*$ is of weak type $L\log\log L(\mathbb{R}^d)$. Furthermore, for $w\in A_1$ and $\Omega\in…

We present a new proof of the classical weak-type $(1,1)$ estimate for Calder\'on-Zygmund operators. This proof is inspired by ideas of Nazarov, Treil, and Volberg that address the non-doubling setting. An application to a weighted…

In this article, we prove weak type $(1,1)$ bounds for the variation and jump operators corresponding to the family of truncations of singular integrals with rough kernels. This resolves an open question raised by Jones, Seeger and Wright…

The purpose of this paper is to establish the weighted norm inequalities of one-sided oscillatory integral operators by the aid of interpolation of operators with change of measures.

We provide quantitative weighted weak type estimates for non-integral square functions in the critical case $p=2$ in terms of the $A_p$ and reverse H\"older constants associated to the weight. The method of proof uses a decoupling of the…