Related papers: Boundedness of commutator generated by fractional …

We establish weighted inequalities for $BMO$ commutators of sublinear operators for all $0<p<\infty$. For weights $w$ satisfying the doubling condition of order $q$ with $0<q<p$ and the reverse H\"{o}lder condition, we prove that $\bullet$…

Let $\phi: \mathbb{R}^n\times[0,\fz)\rightarrow[0,\fz)$ be a function such that $\phi(x,\cdot)$ is an Orlicz function and $\phi(\cdot,t)\in A^{\mathop\mathrm{loc}}_{\infty}(\mathbb{R}^n)$ (the class of local weights introduced by V. S.…

In this paper, boundedness of Hausdorff operator on weak central Morrey space is obtained. Furthermore, we investigate the weak bounds of p- adic fractional Hausdorff Operator on weighted p-adic weak Lebesgue Space. We also obtain the…

For $\mathbb B^n$ the unit ball of $\mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^\Phi_\alpha$, which are generalizations of classical Bergman spaces. We characterize the dual space of large Bergman-Orlicz…

In this article, the authors establish a general (two-weight) boundedness criterion for a pair of functions, $(F,f)$, on $\mathbb{R}^n$ in the scale of weighted Lebesgue spaces, weighted Lorentz spaces, (Lorentz--)Morrey spaces, and…

We provide explicit formulas for the norm of bounded linear functionals on Orlicz-Lorentz function spaces $\Lambda_{\varphi,w}$ equipped with two standard Luxemburg and Orlicz norms. Any bounded linear functional is a sum of regular and…

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, we prove the boundedness of multilinear fractional integral operators from products of Hardy spaces associated with ball quasi-Banach function spaces into their corresponding ball quasi-Banach function spaces. As…

In this paper, we are interested in the following bilinear fractional integral operator $B\mathcal{I}_\alpha$ defined by \[ B\mathcal{I}_{\alpha}({f,g})(x)=\int_{% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion…

We show that if an operator T is bounded on weighted Lebesgue space L^2(w) and obeys a linear bound with respect to the A_2 constant of the weight, then its commutator [b,T] with a function b in BMO will obey a quadratic bound with respect…

It is established $L^{p}$ estimates for the fractional $\Phi$-Laplacian operator defined in bounded domains where the nonlinearity is subcritical or critical in a suitable sense. Furthermore, using some fine estimates together with the…

In this article, we investigate the existence of closed vector subspaces (i.e.spaceability) in various nonlinear subsets of Orlicz-Lorentz spaces $\Lambda_{\varphi,w}$, equipped with the Luxemburg norm. If a family of Orlicz functions…

We study singular integral operators with variable Calder\'on--Zygmund kernels and their commutators with $VMO$ functions in the framework of Orlicz spaces. After revisiting the classical $L^p$ theory, we establish boundedness results in…

Let $L=-\Delta+V$ be a Schr\"odinger operator acting on $L^2(\mathbb R^n)$, $n\ge1$, where $V\not\equiv 0$ is a nonnegative locally integrable function on $\mathbb R^n$. In this paper, we first define molecules for weighted Hardy spaces…

We obtain sufficient and necessary conditions on weight functions $s_1(t),\ldots,s_m(t)$ and $\psi(t)$ so that the weighted multilinear Hardy-Ces\`{a}ro operator \[(f_1,\ldots,f_m)\mapsto \int_{[0,1]^n}\left(\prod_{k=1}^nf_k\left(s_k(t)…

We study the action of Fourier Integral Operators (FIOs) of H{\"o}rmander's type on ${\mathcal{F}} L^p({\mathbb {R}}^d_{comp}$, $1\leq p\leq\infty$. We see, from the Beurling-Helson theorem, that generally FIOs of order zero fail to be…

We prove that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$ and a maximally modulated Calder\'on-Zygmund singular integral operator…

We extend the recently much-studied Hardy factorization theorems to the weight case. The key point of this paper is to establish the factorization theorems without individual condition on the weight functions. As a direct application, we…

Let $(\Omega,\Sigma,\mu)$ be a $\sigma$-finite complete measure space, $\tau:\Omega\rightarrow\Omega$ be a measurable transformation and $\phi$ be an Orlicz function. In this article, first a necessary and sufficient condition for the…

The analysis of Morrey spaces, generalized Morrey spaces and $BMO_\phi$ spaces related to the Dunkl operators on $\mathbb{R}$ are covered in this paper. We prove the boundedness of the Hardy-Littlewood maximal operators, Bessel-Riesz…