Annals of Functional Analysis

Atomic decomposition of variable Hardy spaces via Littlewood–Paley–Stein theory

Jian Tan

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Abstract

The purpose of this paper is to give a new atomic decomposition for variable Hardy spaces via the discrete Littlewood–Paley–Stein theory. As an application of this decomposition, we assume that T is a linear operator bounded on Lq and Hp(), and we thus obtain that T can be extended to a bounded operator from Hp() to Lp().

Article information

Source
Ann. Funct. Anal., Volume 9, Number 1 (2018), 87-100.

Dates
Received: 21 September 2016
Accepted: 23 February 2017
First available in Project Euclid: 14 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.afa/1502697622

Digital Object Identifier
doi:10.1215/20088752-2017-0026

Mathematical Reviews number (MathSciNet)
MR3758745

Zentralblatt MATH identifier
06841343

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Secondary: 47A30: Norms (inequalities, more than one norm, etc.) 42B30: $H^p$-spaces

Keywords
variable exponent atomic decomposition Hardy spaces Littlewood–Paley–Stein functions

Citation

Tan, Jian. Atomic decomposition of variable Hardy spaces via Littlewood–Paley–Stein theory. Ann. Funct. Anal. 9 (2018), no. 1, 87--100. doi:10.1215/20088752-2017-0026. https://projecteuclid.org/euclid.afa/1502697622


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