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Lipschitz conditions satisfied by Hankel transforms

  • P. Heywood (a1) and P. G. Rooney (a2)


It is shown that Hankel transforms of functions on certain weighted LP spaces satisfy Lipschitz and integral Lipschitz conditions. In particular, Fourier-cosine and Fourier-sine transforms satisfy such Lipschitz conditions on such spaces.



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1Hardy, G. H. and Littlewood, J. E.. Some properties of fractional integrals I. Math. Z. 27 (1928), 565606.
2Hardy, G. H., Littlewood, J. E. and Polya, G.. Inequalities (Cambridge; Cambridge University Press, 1967).
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5Rooney, P. G.. On the range of the Hankel transformation. Bull. London Math. Soc. 11 (1979), 45–8.
6Rooney, P. G.. On the Yv and Hv transformations. Canad. J. Math. 32 (1980), 1021–44.


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