Related papers: Fractional Bloom boundedness and compactness of co…

In this paper, we first introduce some new classes of weighted amalgam spaces. Then we give the weighted strong-type and weak-type estimates for fractional integral operators $I_\gamma$ on these new function spaces. Furthermore, the…

The optimal sufficient conditions for the $L^p$-to-$L^q$ compactness of commutators of singular integral operators of both Calder\'on-Zygmund and of rough type are shown in the different exponent ranges $``q>p"$, $``q=p"$ and $``q<p"$ to…

A new characterization of CMO(R^n) is established by the local mean oscillation. Some characterizations of iterated compact commutators on weighted Lebesgue spaces are given, which are new even in the unweighted setting for the first order…

We prove continuity properties of higher order commutators of fractional operators on the multilinear setting, between a product of weighted Lebesgue spaces into certain weighted Lipschitz spaces. The considered operators include the…

Let $\mathcal L=-\Delta+V$ be a Schr\"odinger operator on $\mathbb R^d$, $d\geq3$, where $\Delta$ is the Laplacian operator on $\mathbb R^d$ and the nonnegative potential $V$ belongs to the reverse H\"older class $RH_s$ for $s\geq d/2$. For…

We first consider two types of localizations of singular integral operators of convolution type, and show, under mild decay and smoothness conditions on the auxiliary functions, that their boundedness on the local Hardy space…

Let $L$ be the infinitesimal generator of an analytic semigroup on $L^2(\mathbb{R}^n)$ with Gaussian kernel bounds, and let $L^{-\alpha/2}$ be the fractional integrals of $L$ for $0<\alpha<n$. Assume that $\vec{b}=(b_1,b_2,\cdots,b_m)$ is a…

In this work we obtain boundedness results for fractional operators associated with Schr\"odinger operators $\ \mathcal{L}=-\Delta+V$ on weighted variable Lebesgue spaces. These operators include fractional integrals and their respective…

Let $\mathrm{RBMO}(\mu) = \mathrm{RBMO}(\mathbb{R}^m, \mu)$ denote the regular BMO space introduced by X. Tolsa for an $n$-dimensional finite positive measure on $\mathbb{R}^m$, $0<n \le m$. We characterize the bounded Calder\'on-Zygmund…

Let (G,d) be a first order differential *-calculus on a *-algebra A. We say that a pair (\pi,F) of a *-representation \pi of A on a dense domain D of a Hilbert space and a symmetric operator F on D gives a commutator representation of G if…

Fractional supersymmetric quantum mechanics of order $\lambda$ is realized in terms of the generators of a generalized deformed oscillator algebra and a Z$_{\lambda}$-grading structure is imposed on the Fock space of the latter. This…

This paper gives some characterizations of the boundedness of the maximal or nonlinear commutator of the $p$-adic fractional maximal operator $ \mathcal{M}_{\alpha}^{p}$ with the symbols belong to the $p$-adic BMO spaces on (variable)…

In this paper, we introduce the variable Fofana's spaces $(L^{p(\cdot)},L^q)^\alpha (\mathbb{R}^n)$ where $1< p(\cdot)<\infty$ and $1\leq q,\alpha\leq\infty$, then show some properties and establish the pre-dual of those spaces which are…

We prove that if a weight is a Bekoll\'{e}-Bonami weight for some $q$ and it satisfies another simple condition that depends on $0 < p < \infty$, then the operator taking a function to its harmonic conjugate is bounded on the harmonic…

We establish the equivalent characterisation of the weighted BMO space on the complex plane $\mathbb{C}$ via the two weight commutator of the Beurling--Ahlfors operator with a BMO function. Our method of proofs relies on the explicit kernel…

We show that the product BMO space can be characterized by iterated commutators of a large class of Calder\'on-Zygmund operators. This result follows from a new proof of boundedness of iterated commutators in terms of the BMO norm of their…

Let $T$ be a multilinear operator which is bounded on certain products of unweighted Lebesgue spaces of $\mathbb R^n$. We assume that the associated kernel of $T$ satisfies some mild regularity condition which is weaker than the usual…

In a previous paper by one of us, a "compact version" of Rubio de Francia's weighted extrapolation theorem was proved, which allows one to extrapolate the compactness of an operator from just one space to the full range of weighted spaces,…

Let $0<\alpha<1$ and $\frac{1}{q}=1-\alpha$. We first obtain that the function $\omega :\mathbb{Z} \rightarrow (0,\infty)$ belongs to weight class of $\mathcal{A} (1,q)(\mathbb{Z})$ if and only if discrete fractional maximal operator…

We give a new formulation of the $T1$ theorem for compactness of Calder\'on-Zygmund singular integral operators. In particular, we prove that a Calder\'on-Zygmund operator $T$ is compact on $L^2(\mathbb{R}^n)$ if and only if $T1,T^*1\in…