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Density of analytic polynomials in abstract Hardy spaces
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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.
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Banach function space Rearrangement-invariant space Variable Lebesgue space Abstract Hardy space Analytic polynomial Fejér kernel