# 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

### Keywords

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