Abstract:Let M X(R) be the Banach algebra of all Fourier multipliers on a Banach function space X(R) such that the Hardy-Littlewood maximal operator is bounded on X(R) and on its associate space X (R). For two sets Ψ, Ω ⊂ M X(R) , let Ψ Ω be the set of those c ∈ Ψ for which there exist d ∈ Ω such that the multiplier norm of χ R\[−N,N ] (c − d) tends to zero as N → ∞.In this case we say that the Fourier multiplier c is equivalent at infinity to the Fourier multiplier d. We show that if Ω is a unital Banach subalgebra of… Show more
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