Abstract
Inequalities involving the Fourier transform and its variants have been an essential part of Fourier analysis from its early beginnings. This is not surprising because the size and estimate of the Fourier transform in various function spaces is significant in the development of harmonic analysis and is underscored by the numerous applications they yield in science and engineering. The first LP-estimate of the Fourier transform involving power weights are the results of Paley-Titchmarsh (1934) with extensions by Pitt (1937), Stein (1956) and Rooney (1966). Somewhat more general weights were considered by Hirschman (1957) and Flett (1973).
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Heinig, H.P. (1990). Weighted Inequalities in Fourier Analysis. In: Krbec, M., Kufner, A., Opic, B., RákosnÃk, J. (eds) Nonlinear Analysis, Function Spaces and Applications Vol. 4. TEUBNER-TEXTE zur Mathematik. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-01272-6_2
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DOI: https://doi.org/10.1007/978-3-663-01272-6_2
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