When does the norm of a Fourier multiplier dominate its L∞ norm?

DOI10.1112/PLMS.12206zbMath1412.42034arXiv1712.07609OpenAlexW2962685912MaRDI QIDQ5741851

Eugene Shargorodsky, Alexei Yu. Karlovich

Publication date: 15 May 2019

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.07609

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Multipliers for harmonic analysis in several variables (42B15)

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Algebras of convolution type operators with continuous data do not always contain all rank one operators ⋮ The Brown-Halmos theorem for a pair of abstract Hardy spaces ⋮ Algebras of continuous Fourier multipliers on variable Lebesgue spaces ⋮ The Coburn lemma and the Hartman-Wintner-Simonenko theorem for Toeplitz operators on abstract Hardy spaces ⋮ Bounded compact and dual compact approximation properties of Hardy spaces: new results and open problems ⋮ Invertibility of Fourier convolution operators with \textit{pc} symbols on variable Lebesgue spaces with Khvedelidze weights ⋮ Semi-almost periodic Fourier multipliers on rearrangement-invariant spaces with suitable Muckenhoupt weights ⋮ Unnamed Item ⋮ Banach algebras of Fourier multipliers equivalent at infinity to nice Fourier multipliers ⋮ Calkin images of Fourier convolution operators with slowly oscillating symbols ⋮ Wavelet bases in Banach function spaces ⋮ Noncompactness of Fourier convolution operators on Banach function spaces ⋮ A lower estimate for weak-type Fourier multipliers

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