Interpolation of Lorentz martingale spaces
type: Item
instance of: scholarly article
title: Interpolation of Lorentz martingale spaces
zbMATH Open document ID: 1273.60051
published in: Science China. Mathematics
publication date: 2013-01-28T00:00:00Z
review text: The interpolation spaces are defined by a function parameter \(\varphi\), \[ { \| f \|}_{{(A_0,A_1)}_{\varphi ,q}}:= \left( \int_0^\infty \left(\frac{K(t,f,A_0,A_1)}{\varphi(t)} \right) ^q \, {{dt} \over {t}} \right)^{1/q} \] with a suitable function \(\varphi\), where \(K(t,f,A_0,A_1) := \inf_{f=f_0+f_1} \left\{ \|f_0\|_{A_0} + t\|f_1\|_{A_1} \right\}\), \(0< \theta <1\) and \(0<q \leq \infty \). Similarly, Lorentz spaces and martingale Hardy-Lorentz spaces are introduced with the help of a function parameter. The interpolation spaces between different martingale Hardy-Lorentz spaces are characterized.
reviewed by: Ferenc Weisz
Mathematics Subject Classification ID: 60G42
Mathematics Subject Classification ID: 46B70
zbMATH DE Number: 6131104
zbMATH Keywords: martingale Hardy space
zbMATH Keywords: Lorentz space
zbMATH Keywords: real interpolation
zbMATH Keywords: function parameter
author: Yanbo Ren
author: Tiexin Guo
MaRDI profile type: Publication
full work available at URL: s11425-012-4397-8
OpenAlex ID: W2269028688
cites work: Q4112938
cites work: Recent developments in the theory of Lorentz spaces and weighted inequalities
cites work: Interpolation of classical Lorentz spaces
cites work: Interpolation restricted to decreasing functions and Lorentz spaces
cites work: Lorentz martingale spaces and interpolation
cites work: Interpolation of Quasi-Normed Spaces.
cites work: Interpolation on weak martingale Hardy space
cites work: Interpolation for weak Orlicz spaces with \(M_{\Delta }\) condition
cites work: Q4084797
cites work: On a class of interpolation spaces
cites work: Q3135095
cites work: Q3828540
cites work: Q3336223
cites work: Interpolation with a parameter function.
cites work: Martingale Hardy spaces and their applications in Fourier analysis
DOI: 10.1007/S11425-012-4397-8
description: scientific article; zbMATH DE number 6131104