Related papers: Quantitative weighted estimates for rough homogene…
We consider $A_1$-weights and prove weighted weak type $(1,1)$ estimates for oscillatory singular integrals with kernels satisfying a Dini condition.
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 paper, the main purpose is to consider a number of results concerning boundedness of multilinear fractional Calder\'{o}n-Zygmund operators with kernels of mild regularity. Let $T_{\alpha}$ be a multilinear fractional…
For doubling weights, we obtain a necessary and sufficient condition such that the one weighted inequality of the integral operator induced by Hardy kernels on the unit disk holds. This confirms a conjecture by Guo and Wang in such…
In the paper two-weighted norm estimates with general weights for Hardy-type transforms, maximal functions, potentials and Calder\'on-Zygmund singular integrals in variable exponent Lebesgue spaces defined on quasimetric measure spaces $(X,…
We study the weighted boundedness of the Cauchy singular integral operator $S_\Gm$ in Morrey spaces $L^{p,\lambda}(\Gm)$ on curves satisfying the arc-chord condition, for a class of "radial type" almost monotonic weights. The non-weighted…
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…
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…
A characterization is obtained for those pairs of weights $v$ and $w$ on $\mathbb{R}^2_+$, for which the two--dimensional rectangular integration operator is bounded from a weighted Lebesgue space $L^p_v(\mathbb{R}^2_+)$ to…
Let $t\in(0,\infty)$, $p\in(1,\infty)$, $q\in[1,\infty]$, $w\in A_p$ and $v\in A_q$. We introduce the weighted amalgam space $(L^p,L^q)_t(\mathbb R^n)$ and show some properties of it. Some estimates on these spaces for the classical…
In this paper, we systematically study weighted jump and variational inequalities for rough operators. More precisely, we show some weighted jump and variational inequalities for the families $\mathcal T:=\{T_\varepsilon\}_{\varepsilon>0}$…
For a general Calderon-Zygmund operator $T$ on $R^N$, it is shown that $\|Tf\|_{L^2(w)}\leq C(T)\|w\|_{A_2}\|f\|_{L^2(w)}$ for all Muckenhoupt weights $w\in A_2$. This optimal estimate was known as the $A_2$ conjecture. A recent result of…
We study the approximation numbers of weighted composition operators $f\mapsto w\cdot(f\circ\varphi)$ on the Hardy space $H^2$ on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers…
We present a framework based on modified dyadic shifts to prove multiple results of modern singular integral theory under mild kernel regularity. Using new optimized representation theorems we first revisit a result of Figiel concerning the…
We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition operators. Then, we provide a…
In this paper, we characterize all closed linear operators in a separable Hilbert space which are unitarily equivalent to an integral bi-Carleman operator in $L_2(R)$ with bounded and arbitrarily smooth kernel on $R^2$. In addition, we give…
Let $\T (0\leq \alpha <n)$ be the singular and fractional integrals with variable kernel $\Omega(x,z)$, and $[b,\T]$ be the commutator generated by $\T$ and a Lipschitz function $b$. In this paper, the authors study the boundedness of…
In this paper, we study sharp bound on higher-dimensional Lebesgue product space for Hardy operator on Heisenberg group, the constants of sharp bounds are obtained. In addition, we also give the boundedness for weighted Hardy operator and…
The concepts of weighted numerical radius has been defined in recent times. In this article, we obtain several upper bound for weighted numerical radius of operators and $2 \times 2$ operator matrices which generalize and improves some well…
In this paper, we give a characterization of all closed linear operators in a separable Hilbert space which are unitarily equivalent to an integral operator in $L_2(R)$ with bounded and arbitrarily smooth Carleman kernel on $R^2$. In…