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Lipschitz conditions satisfied by Hankel transforms

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

Abstract

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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References

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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).
3Rooney, P. G.. On the ranges of certain fractional integrals. Canad. J. Math. 24 (1972), 1198–216.
4Rooney, P. G.. A technique for studying the boundedness and extendability of certain types of operators. Canad. J. Math. 25 (1973), 1090–102.
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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