Related papers: Mixed inequalities for commutators with multilinea…

Let $(\mathcal{X},d,\mu)$ be a metric measure space satisfying the so-called upper doubling condition and the geometrically doubling condition. Let $T$ be a Calder\'{o}n-Zygmund operator with kernel satisfying only the size condition and…

We set up some weighted norm inequalities for fractional oscillatory integral operators. As applications, the corresponding results for commutators formed by $BMO(\mathbb{R}^{n})$ functions and the operators are established.

We extend the classical regularity theorem of elliptic operators to maximally hypoelliptic differential operators. More precisely, given vector fields $X_1,\ldots,X_m$ on a smooth manifold which satisfy H\"ormander's bracket generating…

Let $A$ be a positive bounded linear operator on a complex Hilbert space $\mathcal{H}$ and $\mathcal{B}_{A}(\mathcal{H})$ be the subspace of all operators which admit $A$-adjoints operators. In this paper, we establish some inequalities…

Let $K$ be the Calder\'on-Zygmund convolution kernel on $\mathbb{R}^d (d\geq2)$. Define the commutator associated with $K$ and $a\in L^\infty(\mathbb{R}^d)$ by \[ T_af(x)=p.v. \int K(x-y)m_{x,y}a\cdot f(y)dy. \] Recently, Grafakos and…

Paraproducts are a special subclass of the multilinear Calder\'on-Zygmund operators, and their Lebesgue space estimates in the full multilinear range are characterized by the $\mathrm{BMO}$ norm of the symbol. In this note, we characterize…

Given a Radon measure $\mu$ on $R^d$, which may be non doubling, we introduce a space of type BMO with respect to this measure. It is shown that many properties that hold when $\mu$ is doubling remain valid for the space BMO introduced in…

In this paper we solve several problems concerning joint similarity to n-tuples of operators in noncommutative varieties in $[B(\cH)^n]_1$ associated with positive regular free holomorphic functions in $n$ noncommuting variables and with…

In this paper, we develop a comprehensive weighted theory for a class of Banach-valued multilinear bounded oscillation operators on measure spaces, which merges multilinear Calder\'{o}n-Zygmund operators with a quantity of operators beyond…

In this paper, we focus on a class of fractional type integral operators that can be served as extensions of Riesz potential with kernels $$K(x,y)=\frac{\Omega_1(x-A_1 y)}{|x-A_1 y |^{\frac{n}{q_1}}} \cdots \frac{\Omega_m(x-A_m y)}{|x-A_m y…

The main theme of this paper is to give sufficient conditions for the weighted boundedness of the bilinear fractional integral operator $\mathsf{BI}_\al$. The proposed condition involves the union of multilinear Muckenhoupt-type conditions.…

We improve on several weighted inequalities of recent interest by replacing a part of the A_p bounds by weaker A_\infty estimates involving Wilson's A_\infty constant \[ [w]_{A_\infty}':=\sup_Q\frac{1}{w(Q)}\int_Q M(w\chi_Q). \] In…

In this article we prove weighted norm inequalities and pointwise estimates between the multilinear fractional integral operator and the multilinear fractional maximal. As a consequence of these estimations we obtain weighted weak and…

We construct a slightly new noncommutative Calder\'on-Zygmund decomposition by further splitting the bad function. Using this tool, we prove the weak type (1,1) boundedness of noncommutative Calder\'on-Zygmund operators under a class of…

In this paper, the authors establish the existence and boundedness of multilinear Littlewood--Paley operators on products of BMO spaces, including the multilinear $g$-function, multilinear Lusin's area integral and multilinear…

Let $1<p<\infty$. We show the boundedness of operator-valued commutators $[\pi_a,M_b]$ on the noncommutative $L_p(L_\infty(\mathbb{R})\otimes \mathcal{M})$ for any von Neumann algebra $\mathcal{M}$, where $\pi_a$ is the $d$-adic martingale…

In this paper, we present some upper bounds for unitarily invariant norms inequalities. Among other inequalities, we show some upper bounds for the Hilbert-Schmidt norm. In particular, we prove \begin{align*} \|f(A)Xg(B)\pm…

Let $(\cx,\,d,\,\mu)$ be a metric measure space and satisfy the so-called upper doubling condition and the geometrically doubling condition. In this paper, the authors show that for the maximal Calder\'on-Zygmund operator associated with a…

Let $0<\alpha<n$ and $I_\alpha$ be the fractional integral operator. In this paper, we shall use a unified approach to show some boundedness properties of commutators $[b,I_\alpha]$ on the weighted Morrey spaces $L^{p,\kappa}(w)$ under…

We solve a long-standing open problem in theory of weighted inequalities concerning iterated Copson operators. We use a constructive approximation method based on a new discretization principle that is developed here. In result, we…