Related papers: Interpolation between $H^{p(\cdot)}(\mathbb R^n)$ …

In this paper, we introduce the Carleson measure spaces with variable exponents $CMO^{p(\cdot)}$. By using discrete Littlewood$-$Paley$-$Stein analysis as well as Frazier and Jawerth's $\varphi-$transform in the variable exponent settings,…

Let $p(\cdot):\ \mathbb R^n\to(0,1]$ be a variable exponent function satisfying the globally $\log$-H\"older continuous condition and $L$ a non-negative self-adjoint operator on $L^2(\mathbb R^n)$ whose heat kernels satisfying the Gaussian…

In this paper, we investigate the two-weight Hardy inequalities on metric measure space possessing polar decompositions for the case $p=1$ and $1 \leq q <\infty.$ This result complements the Hardy inequalities obtained in \cite{RV} in the…

For $0<p<\infty $ and $\alpha >-1$ the space of Dirichlet type $\mathcal D^p_\alpha $ consists of those functions $f$ which are analytic in the unit disc $\mathbb D$ and satisfy $\int_{\mathbb D}(1-| z| )^\alpha| f^\prime (z)|…

After a review of the reproducing kernel Banach space framework and semi-inner products, we apply the techniques to the setting of Hardy spaces $H^p$ and Bergman spaces $A^p$, $1<p<\infty$, on the unit ball in $\mathbb{C}^n$, as well as the…

We consider the problem of complex interpolation of certain Hardy-type subspaces of K\"othe function spaces. For example, suppose $X_0$ and $X_1$ are K\"othe function spaces on the unit circle $\bold T,$ and let $H_{X_0}$ and $H_{X_1}$ be…

This paper can be considered as the sequel of [6], where the authors have proposed an abstract construction of Hardy spaces H^1. They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more…

Given a finite set $\sigma$ of the unit disc $\mathbb{D}$ and a holomorphic function $f$ in $\mathbb{D}$ which belongs to a class $X$ we are looking for a function $g$ in another class $Y$ which minimizes the norm $|g|_{Y}$ among all…

We study certain interpolation and extension properties of the space of regular operators between two Banach lattices. Let $R_p$ be the space of all the regular (or equivalently order bounded) operators on $L_p$ equipped with the regular…

Motivated by a discrete inequality problem proposed by Duanyang Zhang as Problem 6 of the 2022 Spring NSMO, we prove a median version of Hardy's inequality. For a nonnegative function $f\in L^p(0,\infty)$, $p>1$, let $A(t)$ be the average…

This paper gives a systematic study of operator-valued local Hardy spaces. These spaces are localizations of the Hardy spaces defined by Tao Mei, and share many properties with Mei's Hardy spaces. We prove the ${\rm h}_1$-$\rm bmo$ duality,…

Let $p\in(0,1]$, $q\in(0,\infty]$ and $A$ be a general expansive matrix on $\mathbb{R}^n$. The authors introduce the anisotropic Hardy-Lorentz space $H^{p,q}_A(\mathbb{R}^n)$ associated with $A$ via the non-tangential grand maximal function…

We derive a number of equivalent criterions for the variable exponent Hardy type inequality |\frac{1}{x}\int_{0}^{x}f(t)dt|_{L^{p(.)}(0,1)}\leq C|f|_{L^{p(.)}(0,1)}; f\geq 0. to hold, whenever the exponent $p:(0,1)\to (1,\infty)$ is…

In this article we present a new proof of a sharp Reverse H\"older Inequality for $A_\infty$ weights that is valid in the context of spaces of homogeneous type. Then we derive two applications: a precise open property of Muckenhoupt classes…

This document presents an elementary approach using $\varepsilon$-Poincar\'e inequality to prove generation of $L^{p}$-bounds, $p\in(1,\infty)$, for the homogeneous Landau equation with moderate soft potentials $\gamma\in[-2,0)$. The…

We give a simple explicit description of the norm in the complex interpolation space $(C_p[L_p(M)], R_p[L_p(M)])_\theta$ for any von Neumann algebra $M$ and any $1\le p\le\infty$.

We prove various equivalent characterisations of the Hardy space $H^p_{\mathcal{L}}(\mathbb{C}^n)$ for $0<p<1$ associated with the twisted Laplacian $\mathcal{L}$ which generalises the result of [MPR81] for the case $p=1$. Using the atomic…

In this article, we give a short proof of Hardy's inequality for Hermite expansions of functions in the classical Hardy spaces $H^p({\mathbb R^n})$, by using an atomic decomposition of the Hardy spaces associated with the Hermite operators.…

Let $B_{\alpha}^{p}$ be the space of $f$ holomorphic in the unit ball of $\Bbb C^n$ such that $(1-|z|^2)^\alpha f(z) \in L^p$, where $0<p\leq\infty$, $\alpha\geq -1/p$ (weighted Bergman space). In this paper we study the interpolating…

Let $A$ be a sequence of points of $\mathbb{B}^n$ the unit ball in $\mathbb{C}^n.$ In terms of interpolating vectorial function (or Amar's function)[1], we give a necessary condition on $A$ to be interpolating for the weighted Bergman space…