Karlovich, Alexei2019-05-022019-05-022017PURE: 11665385PURE UUID: bd62a0d1-09ed-4c14-835e-0b26b5df872ahttp://hdl.handle.net/10362/68437Sem PDF conforme despacho.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.350587engBanach function spaceRearrangement-invariant spaceVariable Lebesgue spaceAbstract Hardy spaceAnalytic polynomialFejér kerneljournal article10.14708/cm.v57i2.4364