@inbook{5e0e9678a0794746981c877896c245f2,

title = "Fourier Convolution Operators with Symbols Equivalent to Zero at Infinity on Banach Function Spaces",

abstract = "We study Fourier convolution operators W0(a) with symbols equivalent to zero at infinity on a separable Banach function space X(ℝ) such that the Hardy-Littlewood maximal operator is bounded on X(ℝ) and on its associate space X′(ℝ). We show that the limit operators of W0(a) are all equal to zero.",

keywords = "Banach function space, Equivalence at infinity, Fourier convolution operator, Fourier multiplier, Hardy-Littlewood maximal operator, Limit operator",

author = "Fernandes, {C. A.} and Karlovich, {A. Yu.} and Karlovich, {Yu. I.}",

note = "Funding Information: Acknowledgments This work was partially supported by the Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia (Portuguese Foundation for Science and Technology) through the projects UID/ MAT/00297/2019 (Centro de Matem{\'a}tica e Aplica{\c c}{\~o}es). The third author was also supported by the SEP-CONACYT Project A1-S-8793 (M{\'e}xico). Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2022",

doi = "10.1007/978-3-030-87502-2_34",

language = "English",

isbn = "978-3-030-87501-5",

series = "Trends in Mathematics",

publisher = "Springer",

pages = "335--343",

editor = "Paula Cerejeiras and Michael Reissig and Sabadini, {Irene } and Toft, {Joachim }",

booktitle = "Current Trends in Analysis, its Applications and Computation",

address = "Netherlands",

}