Density of analytic polynomials in abstract Hardy spaces

Alexei  Karlovich

doi:10.14708/cm.v57i2.4364

Density of analytic polynomials in abstract Hardy spaces

Alexei Karlovich

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Abstract

Let \(X\) be a separable Banach function space on the unit circle \(\T\) and let \(H[X]\) be the abstract Hardy space built upon \(X\). We show that the set of analytic polynomials is dense in \(H[X]\) if the Hardy\polishendash Littlewood maximal operator is bounded on the associate space \(X'\). This result is specified to the case of variable Lebesgue spaces.

Original language	English
Pages (from-to)	131-141
Journal	Commentationes Mathematicae
Volume	57
Issue number	2
DOIs	https://doi.org/10.14708/cm.v57i2.4364
Publication status	Published - 2017

Keywords

Banach function space
Rearrangement-invariant space
Variable Lebesgue space
Abstract Hardy space
Analytic polynomial
Fejér kernel

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ASMPS-Karlovich-2017-04-05

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KW - Rearrangement-invariant space

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KW - Abstract Hardy space

KW - Analytic polynomial

KW - Fejér kernel

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Density of analytic polynomials in abstract Hardy spaces

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