Density of analytic polynomials in abstract Hardy spaces

• Autorzy: Alexei Yu. Karlovich
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Banach function space; rearrangement-invariant space; variable Lebesgue space; abstract Hardy space; analytic polynomial; Fejér kernel

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2017
• Tom: 57
• Numer: 2

Daty

wydano

2017

online

2018-03-20

Twórcy

autor

Alexei Yu. Karlovich

Identyfikatory

DOI

10.14708/cm.v57i2.4364