A characterization of the interpolation spaces of \(H^ 1\) and \(L^{\infty}\) on the line
type: Item
instance of: scholarly article
title: A characterization of the interpolation spaces of \(H^ 1\) and \(L^{\infty}\) on the line
zbMATH Open document ID: 0675.46033
DOI: 10.1007/BF02075458
published in: Constructive Approximation
publication date: 1988-01-01T00:00:00Z
review text: It is shown that the spaces \((H^ 1({\mathbb{R}}),L^{\infty}({\mathbb{R}}))\) form a Calderon-Mityagin pair. It follows that the interpolation spaces for this pair consist of elements whose nontangential maximal functions lie in rearrangement invariant spaces.
Mathematics Subject Classification ID: 46M35
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 4105628
zbMATH Keywords: Calderon-Mityagin pair
zbMATH Keywords: interpolation spaces
zbMATH Keywords: nontangential maximal functions
zbMATH Keywords: rearrangement invariant spaces
author: Robert C. Sharpley
reviewed by: Mario Milman
MaRDI profile type: Publication
cites work: K-Divisibility and a Theorem of Lorentz and Shimogaki
cites work: A real variable characterization of $H^{p}$
cites work: K-divisibility of the K-functional and Calderón couples
cites work: Interpolation Between H p Spaces: The Real Method
cites work: Interpolation between \(H^ p \)spaces: The complex method
cites work: Local sharp maximal functions
cites work: Interpolation Theorems for the Pairs of Spaces (L p , L ∞ ) and (L 1 L q )
cites work: Shorter Notes: On the Atomic Decomposition of H 1 and Interpolation
description: scientific article; zbMATH DE number 4105628