Defant, AndreasMastyło, MieczysławPérez Hernández, Antonio2026-02-202026-02-202022-09-01Defant, A., Mastyło, M., Pérez-Hernández, A. (2024). Variants of a Multiplier Theorem of Kislyakov. Journal of the Institute of Mathematics of Jussieu, 23(1), 347–377. URL: https://doi.org/10.1017/S14747480220003911474-7480https://doi.org/10.1017/S1474748022000391https://hdl.handle.net/20.500.14468/31878This is the Accepted Manuscript of an article published by Cambridge University Press in "Journal of the Institute of Mathematics of Jussieu, 23, 2022", available online: https://doi.org/10.1017/S1474748022000391Este es el manuscrito aceptado de un artículo publicado por Cambridge University Press en " Journal of the Institute of Mathematics of Jussieu, 23, 2022", disponible en línea: https://doi.org/10.1017/S1474748022000391We prove stronger variants of a multiplier theorem of Kislyakov. The key ingredients are based on ideas of Kislaykov and the Kahane–Salem–Zygmund inequality. As a by-product we show various multiplier theorems for spaces of trigonometric polynomials on the n-dimensional torus Tn or Boolean cubes {−1, 1}N. Our more abstract approach based on local Banach space theory has the advantage that it allows to consider more general compact abelian groups instead of only the multidimensional torus. As an application we show that various recent ℓ1-multiplier theorems for trigonometric polynomials in several variables or ordinary Dirichlet series may be proved without the Kahane–Salem–Zygmund inequality.eninfo:eu-repo/semantics/openAccess12 MatemáticasartículoFourier analysis on groupsmultipliersSidon setsBoolean functionsmultivariable and Dirichlet polynomials1475-3030