Related papers: Multilinear estimates for maximal rough singular i…

We obtain the optimal open range of $L^{p_1}(\mathbb R^n)\times\cdots\times L^{p_m}(\mathbb R^n)\to L^p(\mathbb R^n)$ bounds for multilinear singular integral operators with homogeneous kernels of the form $\Omega(\frac{y}{|y|})|y|^{-mn}$,…

We study $m$-linear homogeneous rough singular integral operators $\mathcal{L}_{\Omega}$ associated with integrable functions $\Omega$ on $\mathbb{S}^{mn-1}$ with mean value zero. We prove boundedness for $\mathcal{L}_{\Omega}$ from…

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…

In this paper, we study the boundedness properties of the (dyadic) maximal bilinear operator associated with rough homogeneous kernels on $\mathbb{R}$. We establish sharp $L^{p_1}(\mathbb{R}) \times L^{p_2}(\mathbb{R}) \to…

We consider singular integral operators and maximal singular integral operators with rough kernels on homogeneous groups. We prove certain estimates for the operators that imply $L^p$ boundedness of them by an extrapolation argument under a…

Convolution type Calder\'on-Zygmund singular integral operators with rough kernels $\pv \Om(x)/|x|^n$ are studied. A condition on $\Om$ implying that the corresponding singular integrals and maximal singular integrals map $L^p \to L^p$ for…

In this paper, we will give the weighted bounds for multilinear fractional maximal type operators $\mathcal{M}_{\Omega,\alpha}$ with rough homogeneous kernels. We obtain a mixed $A_{(\vec{P},q)}-A_\infty$ bound and a $A_{\vec{P}}$ type…

We study bilinear rough singular integral operators $\mathcal{L}_{\Omega}$ associated with a function $\Omega$ on the sphere $\mathbb{S}^{2n-1}$. In the recent work of Grafakos, He, and Slav\'ikov\'a (Math. Ann. 376: 431-455, 2020), they…

We establish the full quasi-Banach range of $L^{p_1}(\mathbb R) \times L^{p_2}(\mathbb R) \rightarrow L^p(\mathbb R)$ bounds for one-dimensional bilinear singular integral operators with homogeneous kernels whose restriction $\Omega$ to the…

Let $m\in \mathbb{N}$ and $0<\alpha<mn$.In this paper, we will use the idea of Hedberg to reprove that the multilinear operators $\mathcal{T}_{\Omega,\alpha;m}$ and $\mathcal{M}_{\Omega,\alpha;m}$ are bounded from $L^{p_1}(\mathbb…

In this paper, we study the $L^{p}$ boundedness and $L^{p}(w)$ boundedness ($1<p<\infty$ and $w$ a Muckenhoupt $A_{p}$ weight) of fractional maximal singular integral operators $T_{\Omega,\alpha}^{\#}$ with homogeneous convolution kernel…

In dimensions $n\ge 2$ we obtain $L^{p_1}(\mathbb R^n) \times\dots\times L^{p_m}(\mathbb R^n)$ to $L^p(\mathbb R^n)$ boundedness for the multilinear spherical maximal function in the largest possible open set of indices and we provide…

We prove certain $L^p$ estimates ($1<p<\infty$) for non-isotropic singular integrals along surfaces of revolution. As an application we obtain $L^p$ boundedness of the singular integrals under a sharp size condition on their kernels.

Let $\Omega$ be a function on $\mathbb{R}^{mn} $, homogeneous of degree zero, and satisfy a cancellation condition on the unit sphere $\mathbb{S}^{mn-1}$. In this paper, we show that the multilinear singular integral operator \[…

In dimension $n=1$ we obtain $L^{p_1}(\mathbb R) \times\dots\times L^{p_m}(\mathbb R)$ to $L^p(\mathbb R)$ boundedness for the multilinear spherical maximal function in the largest possible open set of indices and we provide counterexamples…

Let $\Omega$ be a function of homogeneous of degree zero and vanish on the unit sphere $\mathbb {S}^n$. In this paper, we investigate the limiting weak-type behavior for singular integral operator $T_\Omega$ associated with rough kernel…

The goal of this paper is to provide a new approach to address the $L^p-$boundedness of bilinear rough singular integral operators. This approach relies on local Fourier series expansion of input functions leading to trilinear estimates…

We prove sparse bounds for maximal oscillatory rough singular integral operator $$T^{P}_{\Omega,*}f(x):=\sup_{\epsilon>0} \left|\int_{|x-y|>\epsilon}e^{\iota P(x,y)}\frac{\Omega\big((x-y)/|x-y|\big)}{|x-y|^{n}}f(y)dy\right|,$$ where…

We establish $L^{p_1}\times\cdots\times L^{p_k}\to L^r$ and $\ell^{p_1}\times\cdots\times \ell^{p_k}\to \ell^r$ type bounds for multilinear maximal operators associated to averages over isometric copies of a given non-degenerate $k$-simplex…

In this paper, we study weighted $L^{p}(w)$ boundedness ($1<p<\infty$ and $w$ a Muckenhoupt $A_{p}$ weight) of singular integrals with homogeneous convolution kernel $K(x)$ on an arbitrary homogeneous group $\mathbb H$ of dimension…