Related papers: Some remarks on extrapolation with "flat" weights

For $0<p\leq\infty$, let $F^{p}_\varphi$ be the Fock space induced by a weight function $\varphi$ satisfying $ dd^c \varphi \simeq \omega_0$. In this paper, given $p\in (0, 1]$ we introduce the concept of weakly localized operators on $…

Let P be a linear, second order, elliptic operator satisfying a Hardy inequality with potential W (i.e. $P-W\geq0$) and best constant $\alpha$. We give conditions so that the spectrum of $W^{-1}P$ is $[\alpha,\infty)$. We apply this to…

We study those smooth complex hypersurfaces W in C^n having the property that all holomorphic functions of finite weighted L^p norm on W extend to entire functions with finite weighted L^p norm. Such hypersurfaces are called interpolation…

The main objective of this work is to bring together two well known and, a priori, unrelated theories dealing with weighted inequalities for the Hardy-Littlewood maximal operator $M$, and thus, we consider the boundedness of $M$ in the…

Let $\Omega \subset \mathbb{R}^{n}$ be bounded a domain. We prove under certain structural assumptions that the fractional maximal operator relative to $\Omega$ maps $L^{p}(\Omega) \to W^{1,p}(\Omega)$ for all $p > 1$, when the smoothness…

We prove that the Hardy-Littlewood maximal operator is bounded in the weighted generalized Orlicz space if the weight satisfies the classical Muckenhoupt condition $A_p$ and $t \to \frac{\varphi(x,t)}{t^p}$ is almost increasing in addition…

A classification of weakly compact multiplication operators on L(L_p), $1<p<\infty$, is given. This answers a question raised by Saksman and Tylli in 1992. The classification involves the concept of $\ell_p$-strictly singular operators, and…

We obtain mixed $A_p$--$A_\infty$ estimates for a large family of multilinear maximal and sparse operators. Operators from this family are known to control for instance multilinear Calder\'on--Zygmund operators, square functions, fractional…

In [Math. Ineq. \& appl., Vol 26 (2) (2023), 511-530] and [Period. Math. Hung., 89 (1) (2024), 116-128], the present author proved that the Riesz potential $I_{\alpha}$ extends to a bounded operator $H^{p(\cdot)}_{\omega}(\mathbb{R}^n) \to…

We prove the sharp mixed $A_{p}-A_{\infty}$ weighted estimate for the Hardy-Littlewood maximal function in the context of weighted Lorentz spaces, namely \[ \|M\|_{L^{p,q}(w)} \lesssim_{p,q,n}…

In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function $\Mm$ introduced in \cite{LOPTT} and for multilinear Calder\'on-Zygmund operators. In particular we obtain a sharp mixed…

Let $A_{\alpha}^{p}(\mathbb{B}^n;\mathbb{C}^d)$ be the weighted Bergman space on the unit ball $\mathbb{B}^n$ of $\mathbb{C}^n$ of functions taking values in $\mathbb{C}^d$. For $1<p<\infty$ let $\mathcal{T}_{p,\alpha}$ be the algebra…

Let $S_{\alpha}$ be the multilinear square function defined on the cone with aperture $\alpha \geq 1$. In this paper, we investigate several kinds of weighted norm inequalities for $S_{\alpha}$. We first obtain a sharp weighted estimate in…

Let $0 < p \leq 1 < q < \infty$ and $\gamma >0$. In this note we discuss the weighted Calder\'on-Hardy spaces on $\mathbb{R}^{n}$, $\mathcal{H}^{p}_{q, \gamma}(\mathbb{R}^{n}, w)$. For $\gamma = 2m$, $m \in \mathbb{N}$, and $n (2m +…

We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including $L^p$-$L^q$, $L^p$-$BMO$ and $L^p$-Lipschitz estimates. The kernels of such operators satisfy…

We construct a topology on the standard Hilbert module $l^2(\mathcal A)$ over a unital $W^*$-algebra $\mathcal A$ such that any "compact" operator, (i.e.\ any operator in the norm closure of the linear span of the operators of the form…

We explore the connection between $p$-regular operators on Banach function spaces and weighted $p$-estimates. In particular, our results focus on the following problem. Given finite measure spaces $\mu$ and $\nu$, let $T$ be an operator…

Bounded and compact generalized weighted composition operators acting from the weighted Bergman space $A^p_\omega$, where $0<p<\infty$ and $\omega$ belongs to the class $\mathcal{D}$ of radial weights satisfying a two-sided doubling…

We characterize the boundedness of Hankel forms and Hankel operators induced by measures on weighted Bergman spaces, where the weights satisfy an upper-doubling condition. We also characterize $A^p_\omega$ Hankel measures for $p\leq 2$. The…

The purpose of this paper is to systematically study compactness and essential norm properties of operators on a very general class of weighted Fock spaces over $\C$. In particular, we obtain rather strong necessary and sufficient…