Related papers: Estimates for Littlewood--Paley Operators on Ball …

This paper establishes that multilinear Calder\'on--Zygmund operators and their maximal operators are bounded on Hardy spaces associated with ball quasi-Banach function spaces. Moreover, we also obtain the boundedness of multilinear…

The note shows that the operator-valued Hardy space $\sH^1$ introduced via Littlewood-Paley $g$-function coincides with the space of $H^1_R(\T, \sL^1)$ of all Bochner integrable operator-valued functions with integrable analytic part. The…

In this paper we consider Littlewood-Paley functions defined by the semigroups associated with the operator $\mathcal{A}=-\frac{\Delta}{2}-x\nabla$ in the inverse Gaussian setting for Banach valued functions. We characterize the uniformly…

Let $T(f)$ denote the Littlewood--Paley square operators, including the Littlewood--Paley $\mathcal{G}$-function $\mathcal{G}(f)$, Lusin's area integral $\mathcal{S}(f)$ and Stein's function $\mathcal{G}^{\ast}_{\lambda}(f)$ with…

Let $L$ be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients on $\mathbb{R}^n$ and $X$ a ball quasi-Banach function space on $\mathbb{R}^n$ satisfying some mild assumptions. Denote by…

We obtain a pointwise description of functions belonging to function spaces with the lattice property. In particular, it is valid for Banach function spaces provided that the Hardy-Littlewood maximal operator is bounded. We also study…

In this article, the authors first introduce a class of Orlicz-slice spaces which generalize the slice spaces recently studied by P. Auscher et al. Based on these Orlicz-slice spaces, the authors introduce a new kind of Hardy type spaces,…

Let $L = \Delta + V$ be a Schr\"odinger operator with a non-negative potential $V$ on a complete Riemannian manifold $M$. We prove that the vertical Littlewood-Paley-Stein functional associated with $L$ is bounded on $L^p(M)$ {\it if and…

We consider the fractional derivative of a general Poisson semigroup. With this fractional derivative we define the generalized fractional Littlewood-Paley $g$-function for semigroups acting on $L^p$-spaces of functions with values in…

Let $L_{1}$ and $L_{2}$ be non-negative self-adjoint operators acting on $L^{2}(X_{1})$ and $L^{2}(X_{2})$, respectively, where $X_{1}$ and $X_{2}$ are spaces of homogeneous type. Assume that $L_{1}$ and $L_{2}$ have Gaussian heat kernel…

Let $\mathcal{E}(X,d,\mu)$ be a Banach function space over a space of homogeneous type $(X,d,\mu)$. We show that if the Hardy-Littlewood maximal operator $M$ is bounded on the space $\mathcal{E}(X,d,\mu)$, then its boundedness on the…

We prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator $T$ in the weighted Lebesgue scale…

Let $\alpha\in{\Bbb R}$, $0<p<\infty$ and $X$ be a ball quasi-Banach function space on ${\Bbb R}^n$. In this article, we introduce the Herz-type space $\dot{K}^{\alpha,p}_X({\Bbb R}^n)$ associated with $X$. We identify the dual space of…

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 consider maximal kernel-operators on abstract measure spaces $(X,\mu)$ equipped with a ball-basis. We prove that under certain asymptotic condition on the kernels those operators maps boundedly BMO(X) into BLO(X), generalizing the…

Let $(\mathbb{X},\,d,\,\mu)$ be a space of homogeneous type in the sense of Coifman and Weiss, $X$ be a ball quasi-Banach function space on $\mathbb{X}$, $L$ be a non-negative self-adjoint operator on $L^2(\mathbb{X})$, and assume that, for…

In this paper we prove off-diagonal, limited range, multilinear, vector-valued, and two-weight versions of the Rubio de Francia extrapolation theorem in general quasi-Banach function spaces. We prove mapping properties of the generalization…

In this paper we establish $L^p(\mathbb{R}^d,\gamma_\infty)$-boundedness properties for square functions involving time and spatial derivatives of Ornstein-Uhlenbeck semigroups. Here $\gamma_\infty$ denotes the invariant measure. In order…

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…

In this paper, we define for the first time the local Morrey-type space associated with ball quasi-Banach function spaces and show the related series of properties. In addition, Hardy-Littlewood maximal operator's boundedness is proved. We…