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Density of analytic polynomials in abstract Hardy spaces

100%

Karlovich A. Y.

Commentationes Mathematicae

2017

tom 57

nr 2

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.

Banach algebra of the Fourier multipliers on weighted Banach function spaces

100%

Karlovich A.

Concrete Operators

2015

tom 2

nr 1

Let MX,w(ℝ) denote the algebra of the Fourier multipliers on a separable weighted Banach function space X(ℝ,w).We prove that if the Cauchy singular integral operator S is bounded on X(ℝ, w), thenMX,w(ℝ) is continuously embedded into L∞(ℝ). An important consequence of the continuous embedding MX,w(ℝ) ⊂ L∞(ℝ) is that MX,w(ℝ) is a Banach algebra.

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1 Commentationes Mathematicae

1 Concrete Operators

1 Karlovich A.

1 Karlovich A. Y.

1 2017

1 2015

Wyniki wyszukiwania

Density of analytic polynomials in abstract Hardy spaces

Banach algebra of the Fourier multipliers on weighted Banach function spaces