Geodesic
On the Hankel and Some Related Transformations
Canadian journal of mathematics, Tome 40 (1988) no. 4, pp. 989-1009

Voir la notice de l'article provenant de la source Cambridge University Press

The transformations we will discuss in this paper are the Hankel transformation Hυ defined for f ∊ C 0, the collection of continuous functions compactly supported in (0, ∞), by (1.1) and the and transformations defined for such f by (1.2) and (1.3) where Jv >and Yv are the Bessel functions of the first and second kinds respectively, and H v is the Struve function; for the theory of these functions see [1, Chapter VII].These transformations were studied extensively by one of us in [5] and [6] on the spaces defined in [7; Sections 1 & 5]. In those papers the boundedness of the three transformations was fully given on the spaces for 1 < p < ∞, but not for p = 1. Also inversion formulae were given for the transformations only for portions of their respective ranges of boundedness. 
Heywood, P.; Rooney, P. G. On the Hankel and Some Related Transformations. Canadian journal of mathematics, Tome 40 (1988) no. 4, pp. 989-1009. doi: 10.4153/CJM-1988-039-2
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[1] 1. Erdelyi, A. et al., Higher transcendental functions I &amp; II (New York, McGraw-Hill, 1953). Google Scholar

[2] 2. Erdelyi, A. et al., Tables of integral transforms I &amp; II (New York, McGraw-Hill, 1954). Google Scholar

[3] 3. Heywood, P. and Rooney, P. G., On the inversion of the even and odd Hilbert transformations, Proc. Roy. Soc. Edinburgh 109A, 201–211. Google Scholar

[4] 4. Rooney, P. G., On the ranges of certain fractional integrals, Can J. Math. 24 (1972), 1198–1216. Google Scholar

[5] 5. Rooney, P. G., A technique for studying the boundedness and extendability of certain types of operators, Can. J. Math. 25 (1973), 1090–1102. Google Scholar

[6] 6. Rooney, P. G., On and transformations, Can. J. Math. 32 (1980), 1021–1044. Google Scholar

[7] 7. Rooney, P. G., On the integral transformations with G-function kernels, Proc. Roy. Soc. Edinburgh 93A (1983), 265–297. Google Scholar

[8] 8. Stein, E. M., Interpolation of linear operators, Trans. Amer. Math. Soc. 87 (1958), 159–172. Google Scholar

[9] 9. Titchmarsh, E. C., The theory of Fourier integrals (Oxford U.P., 1937). Google Scholar

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