The aim of the paper is to highlight some open problems concerning approximation
properties of Hardy spaces. We also present some results on the bounded compact and the …

Let X be a Banach function space on the unit circle T, let X′ be its associate space, and let
H [X] and H [X′] be the abstract Hardy spaces built upon X and X′, respectively. Suppose …

Abstract Let H [X] and H [Y] be abstract Hardy spaces built upon Banach function spaces X
and Y over the unit circle T. We prove an analogue of the Brown–Halmos theorem for …

We show that several definitions of algebras of continuous Fourier multipliers on variable
Lebesgue spaces over the real line are equivalent under some natural assumptions on …

Let X (R) be a separable Banach function space such that the Hardy–Littlewood maximal
operator M is bounded on X (R) and on its associate space X'(R). Suppose that a is a Fourier …

Let Φ be a C∗-subalgebra of L∞(ℝ) L^ ∞ (R) and SOX (ℝ)◇ SO_ X (R)^\diamond be the
Banach algebra of slowly oscillating Fourier multipliers on a Banach function space X (ℝ) X …

Abstract Let X (R) X (R) be a separable Banach function space such that the Hardy-
Littlewood maximal operator is bounded on X (R) X (R) and on its associate space X'(R) …

The Brown–Halmos theorem for discrete Wiener–Hopf operators | Advances in Operator Theory
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Asmar et al.[Note on norm convergence in the space of weak type multipliers. J Operator
Theory. 1998; 39 (1): 139–149] proved that the space of weak-type Fourier multipliers acting …

We say that an operator between Banach spaces is maximally noncompact if its operator
norm coincides with its Hausdorff measure of noncompactness. We prove that a translation …