Spaces of Carleson measures: duality and interpolation
type: Item
instance of: scholarly article
title: Spaces of Carleson measures: duality and interpolation
zbMATH Open document ID: 0638.42020
DOI: 10.1007/BF02384441
published in: Arkiv för Matematik
publication date: 1987-01-01T00:00:00Z
review text: We consider the relationship of tent spaces with spaces of Carleson measures. In particular we identify the spaces of Carleson measures as duals of certain tent spaces. We also compute the real interpolation spaces of some extreme tent spaces. Finally, we outline an extension of our results to product domains. Coifman, Meyer and Stein developed a theory of tent spaces with interesting applications. Their theory has led to a unification and simplification of some basic techniques in harmonic analysis. The theory of tent spaces is closely related to the one of Hardy spaces. As pointed out by Coifman, Meyer and Stein, the interpolation theory of tent spaces can be used to derived the corresponding theory for \(H^ p\) spaces and Lipschitz spaces.
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 4040516
zbMATH Keywords: tent spaces
zbMATH Keywords: spaces of Carleson measures
zbMATH Keywords: interpolation spaces
zbMATH Keywords: \(H^ p\) spaces
zbMATH Keywords: Lipschitz spaces
author: Josefina Alvarez Alonso
author: Mario Milman
MaRDI profile type: Publication
cites work: \(H^ p\) continuity properties of Calderón-Zygmund-type operators
cites work: Mesures de Carleson d'ordre $\alpha$ et solutions au bord de l'équation $\overline\partial$
cites work: An inequality for measures on a half-space.
cites work: Q4112938
cites work: Tent Spaces Based on the Lorentz Spaces
cites work: An atomic decomposition of distributions in parabolic \(H^p\) spaces
cites work: Interpolations by bounded analytic functions and the corona problem
cites work: Carleson measure on the bi-disc
cites work: A continuous version of duality of \(H^ 1\) with BMO on the bidisc
cites work: Some recent developments in Fourier analysis and 𝐻^{𝑝}-theory on product domains
cites work: Some new function spaces and their applications to harmonic analysis.
cites work: Extensions of Hardy spaces and their use in analysis
cites work: Extension of a theorem of Carleson
cites work: \(H^p\) spaces of several variables
cites work: On L(p,q) spaces
cites work: Calderon-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderon
cites work: Fourier Type and Complex Interpolation
cites work: Q5607484
cites work: Q3665720
full work available at URL: https://doi.org/10.1007/bf02384441
OpenAlex ID: W2025663085
description: scientific article; zbMATH DE number 4040516