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Miyachi’s Theorem for the k-Hankel Transform on R^d

Mohamed Amine Boubatra
경북대학교 자연과학대학 수학과|2023.09|Kyungpook Mathematical Journal|제63권 제3호|pp. 425-435|DOI 10.5666/KMJ.2023.63.3.425

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키워드

k-Hankel transformMiyachi’s theoremHardy’s theorem
주제분류수학

초록

The classical Hardy theorem on R states that a function f and its Fourier transform cannot both be very smal simultaneously, this fact was generalized by Miyachi in terms L1 + L∞ and log+-functions. In this paper, we consider the k-Hankel transform which is a deformation of the Hankel transform by a parameter k > 0 arising from Dunkl’s theory. Moreover, we study Miyachi’s theorem for the k-Hankel transform on Rd.

Abstract

The classical Hardy theorem on R states that a function f and its Fourier transform cannot both be very smal simultaneously, this fact was generalized by Miyachi in terms L1 + L∞ and log+-functions. In this paper, we consider the k-Hankel transform which is a deformation of the Hankel transform by a parameter k > 0 arising from Dunkl’s theory. Moreover, we study Miyachi’s theorem for the k-Hankel transform on Rd.

참고문헌 (18)

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