Generalized Poincaré embeddings and weighted Hardy operator on spaces
type: Item
instance of: scholarly article
title: Generalized Poincaré embeddings and weighted Hardy operator on spaces
zbMATH Open document ID: 1201.42015
author: Canqin Tang
author: Zhichun Zhai
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-09-01T00:00:00Z
review text: The well-known Poincaré embedding \(\dot{W}^{1,n}(\mathbb{R}^n)\subset \text{BMO}(\mathbb{R}^n)\) and the John-Nirenberg inequality in \(\text{BMO}(\mathbb{R}^n)\) are useful tools in modern analysis and partial differential equations. The authors establish the generalized Poincaré embeddings and the John-Nirenberg inequality in the \(Q\)-type spaces \(Q^{\alpha, q}_p(\mathbb{R}^n)\) for all \(\alpha \in (0,1)\), \(p\in(0,\infty]\) and \(q\in[1,\infty]\), which generalizes the corresponding classical results on \(\text{BMO}(\mathbb{R}^n)\). Moreover, the authors also give sufficient and necessary conditions on the function \(\psi\) to ensure that the corresponding weighted Hardy operator \(U_\psi\) and its adjoint, the weighted Cesàro average operator \(V_\psi\), are bounded on the spaces \(Q^{\alpha, q}_p(\mathbb{R}^n)\).
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 42B35
zbMATH DE Number: 5777341
zbMATH Keywords: Poincaré embedding
zbMATH Keywords: John-Nirenberg inequality
zbMATH Keywords: weighted Hardy space
zbMATH Keywords: \(Q\)-space
reviewed by: Dachun Yang
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.05.063
OpenAlex ID: W2083725780
cites work: \({\mathcal Q}_p\) spaces in strictly pseudoconvex domains
cites work: Q3331708
cites work: Q5476768
cites work: Some new tent spaces and duality theorems for fractional Carleson measures and \(Q_{\alpha}(\mathbb R^n)\).
cites work: The dyadic structure and atomic decomposition of \(Q\) spaces in several real variables
cites work: Q3425002
cites work: Q spaces of several real variables
cites work: Q4728839
cites work: On functions of bounded mean oscillation
cites work: Generalized Navier-Stokes equations with initial data in local \(Q\)-type spaces
cites work: Predual spaces for \(Q\) spaces
cites work: Paraproducts and Hankel operators of Schatten class via \(p\)-John--Nirenberg theorem
cites work: New applications of Besov-type and Triebel-Lizorkin-type spaces
cites work: Geometric wave equations
cites work: Decomposition theorems for \(\mathcal Q_p\) spaces
cites work: \(L^p\) and BMO bounds of weighted Hardy-Littlewood averages
cites work: A sharp Sobolev trace inequality for the fractional-order derivatives
cites work: Homothetic variant of fractional Sobolev space with application to Navier-Stokes system
cites work: A note on dyadic Hausdorff capacities
cites work: A new class of function spaces connecting Triebel--Lizorkin spaces and \(Q\) spaces
cites work: New Besov-type spaces and Triebel-Lizorkin-type spaces including \(Q\) spaces
cites work: Decompositions of Besov-Hausdorff and Triebel-Lizorkin-Hausdorff spaces and their applications
cites work: A John-Nirenberg type inequality for \(Q_{\alpha}(\mathbb R^n)\)
cites work: Well-posedness for fractional Navier-Stokes equations in critical spaces \(\dot B _{\infty, \infty}^{-(2\beta-1)}(\mathbb R^n)\)
DOI: 10.1016/J.JMAA.2010.05.063
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description: scientific article; zbMATH DE number 5777341