Abstract
We indicate criteria for the coincidence of the Knopp kernels K(f) K(A f), and K (R f) of bounded functions f(t); here,
. In Particular, we prove that K(f) = K(A f) ⇔ K(f) = K(R f).
References
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G. A. Mikhalin, “Conditions for coincidence of the kernel of a sequence with the kernels of its (R, p n, α) and (J, p n) means,” Ukr. Mat. Zh., 31, No. 51, 504–509 (1979).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 12, pp. 1712–1714, December, 1998.
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Usenko, E.G. Criteria for the coincidence of the kernel of a function with the kernels of its Riesz and Abel integral means. Ukr Math J 50, 1952–1955 (1998). https://doi.org/10.1007/BF02514212
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DOI: https://doi.org/10.1007/BF02514212