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We study the rough bilinear singular integral, introduced by Coifman and Meyer , $$ T_\Omega(f,g)(x)=p.v. \! \int_{\mathbb R^{n}}\! \int_{\mathbb R^{n}}\! |(y,z)|^{-2n} \Omega((y,z)/|(y,z)|)f(x-y)g(x-z) dydz, $$ when $\Omega $ is a function…
In this paper, we will use the conclusions and methods in \cite{1} to obtain the sharp bounds for a class of integral operators with the nonnegative kernels in weighted-type spaces on Heisenberg group. As promotions, the sharp bounds of…
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 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…
For any Calder\'on-Zygmund operator $ T$, any weight $ w$, and $ \alpha >1$, the operator $ T$ is bounded as a map from $ L ^{1} (M _{ L \log\log L (\log\log\log L) ^{\alpha } } w )$ into weak-$L^1(w)$. The interest in questions of this…
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 $B_{(n-1)/2}$.…
This article develops a novel approach to the representation of singular integral operators of Calder\'on-Zygmund type in terms of continuous model operators, in both the classical and the bi-parametric setting. The representation is…
We study a class of oscillatory hypersingular integral operators associated to a radial hypersurface of the form $\Gamma(t)=(t,\varphi(t)), t\in\R{n}$. When $\varphi$ satisfies suitable curvature and monotonicity conditions, we prove…
This is a continuation of our previous research about an oscillatory integral operator $T_{\alpha, \beta}$ on compact manifolds $\mathbb{M}$. We prove the sharp $H^{p}$-$L^{p,\infty}$ boundedness on the maximal operator $T^{*}_{\alpha,…
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…
Let $T_\Omega$ be the singular integral operator with variable kernel $\Omega(x,z)$. In this paper, by using the atomic decomposition theory of weighted weak Hardy spaces, we will obtain the boundedness properties of $T_\Omega$ on these…
Let $\Omega$ be homogeneous of degree zero and have mean value zero on the unit sphere ${S}^{n-1}$, $T_{\Omega}$ be the convolution singular integral operator with kernel $\frac{\Omega(x)}{|x|^n}$. For $b\in{\rm BMO}(\mathbb{R}^n)$, let…
The paper deals with the basic integral equation of random field estimation theory by the criterion of minimum of variance of the error estimate. This integral equation is of the first kind. The corresponding integra$ operator over a…
Suppose $L=-\Delta+V$ is a Schr\"odinger operator on $\mathbb{R}^n$ with a potential $V$ belonging to certain reverse H\"older class $RH_\sigma$ with $\sigma\geq n/2$. The main aim of this paper is to provide necessary and sufficient…
We prove weighted weak-type $(r,r)$ estimates for operators satisfying $(r,s)$ limited-range sparse domination of $\ell^q$-type. Our results contain improvements for operators satisfying limited-range and square function sparse domination.…
We study the boundedness of some sublinear operators on weighted Morrey spaces under certain size conditions. These conditions are satisfied by most of the operators in harmonic analysis, such as the Hardy-Littlewood maximal operator,…
We revisit and extend known bounds on operator-valued functions of the type $$ T_1^{-z} S T_2^{-1+z}, \quad z \in \ol \Sigma = \{z\in\bbC\,|\, \Re(z) \in [0,1]\}, $$ under various hypotheses on the linear operators $S$ and $T_j$, $j=1,2$.…
In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces are obtained. The operators include Calder\'on--Zygmund singular integral operator,…
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…
Let $0<\alpha<n$ and $T_{\Omega,\alpha}$ be the homogeneous fractional integral operator which is defined by \begin{equation*} T_{\Omega,\alpha}f(x):=\int_{\mathbb R^n}\frac{\Omega(x-y)}{|x-y|^{n-\alpha}}f(y)\,dy, \end{equation*} where…