Related papers: Three observations on commutators of Singular Inte…

Let $(M,g)$ be a compact Riemannian manifold and $P_1:=-h^2\Delta_g+V(x)-E_1$ so that $dp_1\neq 0$ on $p_1=0$. We assume that $P_1$ is quantum completely integrable in the sense that there exist functionally independent pseuodifferential…

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…

In this article we present two mechanisms for deducing logarithmic quantitative unique continuation bounds for certain classes of integral operators. In our first method, expanding the corresponding integral kernels, we exploit the…

We characterize the compactness of commutators in the Bloom setting. Namely, for a suitably non-degenerate Calder\'on--Zygmund operator $T$, and a pair of weights $ \sigma , \omega \in A_p$, the commutator $ [T, b]$ is compact from $ L ^{p}…

In this paper, the following iterated commutators $T_{*,\Pi b}$ of maximal operator for multilinear singular integral operators and $I_{\alpha, \Pi b}$ of multilinear fractional integral operator are introduced and studied $$\aligned…

In the Standard Model and many of its extensions, it is well known that all of the observables associated with the rare decays $b\to s\gamma$ and $b\to s\ell^+\ell^-$ can be expressed in terms of the three Wilson coefficients,…

We generalize the Lieb-Robinson theorem to systems whose Hamiltonian is the sum of local operators whose commutators are bounded.

In this paper we prove that the space of two parameter, matrix-valued BMO functions can be characterized by considering iterated commutators with the Hilbert transform. Specifically, we prove that $$\| B \|_{BMO} \lesssim \| [[M_B,…

In this paper, we study the boundedness of Bochner-Riesz commutator $$[b, S^{\alpha}(\mathcal{L})](f) = b S^{\alpha}(\mathcal{L})(f) - S^{\alpha}(\mathcal{L})(bf)$$ of a $BMO^{\varrho}(\mathbb{R}^d)$ function $b$ and the Bochner-Riesz…

In this paper, the main aim is to consider the boundedness of commutators of multilinear Calder\'{o}n-Zygmund operators with Lipschitz functions in the context of the variable exponent Lebesgue spaces. Furthermore, the variable versions of…

Linear non-compact operators are difficult to study because they do not exist in the finite dimensional world. Recently, Math\'{e} and Hofmann studied the singular values of the compact composition of the non-compact Hausdorff moment…

We examine dyadic paraproducts and commutators in the non-homogeneous setting, where the underlying Borel measure $\mu$ is not assumed to be doubling. We first establish a pointwise sparse domination for dyadic paraproducts and related…

Let (M,\mu) be a sigma-finite measure space. Let (T_t) be a semigroup of positive preserving maps on (M,\mu) with standard assumptions. We prove a H_1-BMO duality theory with assumptions only on T_t. The BMO is defined as spaces of…

Let $[b,\mathcal T_\alpha]~(0\leq\alpha<n)$ be the commutators generated by $BMO(\mathbb R^n)$ functions and a class of sublinear operators satisfying certain size conditions. The aim of this paper is to study the endpoint estimates of…

Supersymmetry might be broken, in the real world, by anomalies that affect composite operators, while leaving the action supersymmetric. New constraint equations that govern the composite operators and their anomalies are examined. It is…

In this paper, we study the $L^p$-boundedness of the commutator $[b, S_R^\delta(H)](f) = bS_R^\delta(H) f - S_R^\delta(H)(bf)$ of a BMO function $b$ and the Bochner-Riesz means $S_R^\delta(H)$ for Hermite operator $H=-\Delta +|x|^2$ on…

In this paper, we systematically study the Fefferman-Stein inequality and Coifman-Fefferman inequality for the general commutators of singular integral operators that satisfy H\"{o}rmander conditions of Young type. Specifically, we first…

We give two weighted norm estimates for higher order commutator of classical operators such as singular integral and fractional type operators, between weighted $L^p$ and certain spaces that include Lipschitz, BMO and Morrey spaces. We also…

We present a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. Our approach, based on commutator methods, applies to nets of unitary operators, unitary representations of topological…

The goal of this paper is to study the boundedness and compactness of the Bergman projection commutators in two weighted settings via the weighted BMO and VMO spaces, respectively. The novelty of our work lies in the distinct treatment of…