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L p -Boundedness of general index transforms

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Abstract

We establish the boundedness properties in L p for a class of integral transformations with respect to an index of hypergeometric functions. In particular, by using the Riesz-Thorin interpolation theorem, we get the corresponding results in L p (R +), 1 ⩽ p ⩽ 2, for the Kontorovich-Lebedev, Mehler-Fock, and Olevskii index transforms. An inversion theorem is proved for a general index transformation. The case p=2 is known as the Plancherel-type theory for this class of transformations.

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  1. University of Porto, Campo Alegre str., 687, 4169-007, Porto, Portugal

    S. B. Yakubovich

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  1. S. B. Yakubovich
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Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 1, pp. 127–147, January–March, 2005.

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Yakubovich, S.B. L p -Boundedness of general index transforms. Lith Math J 45, 102–122 (2005). https://doi.org/10.1007/s10986-005-0011-x

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  • DOI: https://doi.org/10.1007/s10986-005-0011-x

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