# Density of analytic polynomials in abstract Hardy spaces

Research output: Contribution to journalArticle

### 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 131-141 Commentationes Mathematicae 57 2 https://doi.org/10.14708/cm.v57i2.4364 Published - 2017

### Fingerprint

Banach Function Space
Maximal Operator
Lebesgue Space
Hardy Space
Unit circle
Polynomial

### Keywords

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

### Cite this

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title = "Density of analytic polynomials in abstract Hardy spaces",
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.",
keywords = "Banach function space, Rearrangement-invariant space, Variable Lebesgue space, Abstract Hardy space, Analytic polynomial, Fej{\'e}r kernel",
author = "Alexei Karlovich",
note = "Sem PDF conforme despacho.",
year = "2017",
doi = "10.14708/cm.v57i2.4364",
language = "English",
volume = "57",
pages = "131--141",
journal = "Commentationes Mathematicae",
publisher = "Polish Mathematical Society",
number = "2",

}

In: Commentationes Mathematicae, Vol. 57, No. 2, 2017, p. 131-141.

Research output: Contribution to journalArticle

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T1 - Density of analytic polynomials in abstract Hardy spaces

AU - Karlovich, Alexei

N1 - Sem PDF conforme despacho.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Banach function space

KW - Rearrangement-invariant space

KW - Variable Lebesgue space

KW - Abstract Hardy space

KW - Analytic polynomial

KW - Fejér kernel

U2 - 10.14708/cm.v57i2.4364

DO - 10.14708/cm.v57i2.4364

M3 - Article

VL - 57

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EP - 141

JO - Commentationes Mathematicae

JF - Commentationes Mathematicae

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ER -