Density of analytic polynomials in abstract Hardy spaces

Alexei Yu. Karlovich. "Density of analytic polynomials in abstract Hardy spaces." Commentationes Mathematicae 57.2 (2017): null. <http://eudml.org/doc/292426>.

@article{AlexeiYu2017,
abstract = {Let $X$ be a separable Banach function space on the unit circle $\mathbb \{T\}$ 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 HardyLittlewood maximal operator is bounded on the associate space $X^\{\prime \}$. This result is specified to the case of variable Lebesgue spaces.},
author = {Alexei Yu. Karlovich},
journal = {Commentationes Mathematicae},
keywords = {Banach function space; rearrangement-invariant space; variable Lebesgue space; abstract Hardy space; analytic polynomial; Fejér kernel},
language = {eng},
number = {2},
pages = {null},
title = {Density of analytic polynomials in abstract Hardy spaces},
url = {http://eudml.org/doc/292426},
volume = {57},
year = {2017},
}

TY - JOUR
AU - Alexei Yu. Karlovich
TI - Density of analytic polynomials in abstract Hardy spaces
JO - Commentationes Mathematicae
PY - 2017
VL - 57
IS - 2
SP - null
AB - Let $X$ be a separable Banach function space on the unit circle $\mathbb {T}$ 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 HardyLittlewood maximal operator is bounded on the associate space $X^{\prime }$. This result is specified to the case of variable Lebesgue spaces.
LA - eng
KW - Banach function space; rearrangement-invariant space; variable Lebesgue space; abstract Hardy space; analytic polynomial; Fejér kernel
UR - http://eudml.org/doc/292426
ER -