Abstract
We study the maximal and fractional maximal functions and Riesz potentials that are generated by the generalized shift operator associated with the Laplace-Bessel operator. We obtain some pointwise and integral estimates that give a relation between the B-maximal and B-fractional maximal functions and B-Riesz potentials and extend the available results to the objects of a more general nature. Basing on these results, we prove interpolation theorems for the B-fractional maximal functions and B-Riesz potentials.
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Original Russian Text Copyright © 2008 Guliev V. S., Garakhanova N. N., and Zeren Yu.
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Baku; Urfa. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 6, pp. 1263–1279, November–December, 2008.
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Guliev, V.S., Garakhanova, N.N. & Zeren, Y. Pointwise and integral estimates for the B-Riesz potential in terms of B-maximal and B-fractional maximal functions. Sib Math J 49, 1008–1022 (2008). https://doi.org/10.1007/s11202-008-0097-6
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DOI: https://doi.org/10.1007/s11202-008-0097-6