Abstract
We study Fourier convolution operators W 0(a) with symbols equivalent to zero at infinity on a separable Banach function space \(X(\mathbb {R})\) such that the Hardy-Littlewood maximal operator is bounded on \(X(\mathbb {R})\) and on its associate space \(X'(\mathbb {R})\). We show that the limit operators of W 0(a) are all equal to zero.
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Acknowledgements
This work was partially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the projects UID/ MAT/00297/2019 (Centro de Matemática e Aplicações). The third author was also supported by the SEP-CONACYT Project A1-S-8793 (México).
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Fernandes, C.A., Karlovich, A.Y., Karlovich, Y.I. (2022). Fourier Convolution Operators with Symbols Equivalent to Zero at Infinity on Banach Function Spaces. In: Cerejeiras, P., Reissig, M., Sabadini, I., Toft, J. (eds) Current Trends in Analysis, its Applications and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-87502-2_34
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DOI: https://doi.org/10.1007/978-3-030-87502-2_34
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