Spaces of bounded \(\lambda\)-central mean oscillation, Morrey spaces, and \(\lambda\)-central Carleson measures
type: Item
instance of: scholarly article
title: Spaces of bounded \(\lambda\)-central mean oscillation, Morrey spaces, and \(\lambda\)-central Carleson measures
zbMATH Open document ID: 0948.42013
author: Martha Guzmán-Partida
author: Josefina Alvarez Alonso
author: Joseph Lakey
published in: Collectanea Mathematica
publication date: 2000-11-19T00:00:00Z
full work available at URL: https://eudml.org/doc/41472
review text: We prove that the Morrey space is contained in the space \(\text{CMO}^q\) of functions with bounded central mean oscillation, explaining in this way the dependence of \(\text{CMO}^q\) on \(q\). We also define a natural extension of \(\text{CMO}^2\), to prove the existence of a continuous bijection with central Carleson measures of order \(\lambda\). This connection is further studied to extend and refine duality results involving tent spaces and Hardy spaces associated with Herz-type spaces. Finally, we prove continuity results on these spaces for general non-convolution singular integral operators, including pseudo-differential operators with symbols in the Hörmander class \(S^m_{\rho/\delta}\), \(\rho< 1\), and linear commutators.
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 35S05
zbMATH DE Number: 1454850
zbMATH Keywords: Morrey spaces
zbMATH Keywords: bounded central mean oscillation
zbMATH Keywords: central Carleson measures
zbMATH Keywords: tent spaces
zbMATH Keywords: Hardy spaces
zbMATH Keywords: Herz-type spaces
zbMATH Keywords: non-convolution singular integral operators
zbMATH Keywords: pseudo-differential operators
zbMATH Keywords: commutators
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1454850