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Scientific Bulletin of Namangan State University

Abstract

The obtained results extend the well-known theorem of Hardy-Littlewood for one-dimensional fractional integrals to the case of mixed Hölderness.

First Page

32

Last Page

39

References

1. Vakulov B. G. Operator tipa potenchiala v obobshennx klassax Geldera // Izv. vuz. Matematika. 1986. № 11. S. 66-69. 2. Rubin B. S. Drobne integral v prostranstvax Geldera s vesom i operator tipa potenchiala.// Izv.AN ArmSSR. Matem. 1974. T.3. №4. S.308-324. 3. Rubin B.S. Drobne integral i rissov potenchial s radialnoy plotnostyu v prostranstvax so stepennm vesom// Izv. AN ArmSSR. Mat. 1986. T.21. №5. S. 488-503 4. Samko S.G., Kilbas A.A., Marishev O.I. Integral i proizvodne drobnogo poryadka i nekotore ix prilojeniya. Minsk, "Nauka i Texnika", 1987. 5. H.G.Hardy and J.E.Littelwood. Some properties of fractional integrals. I.//Math. Z. 1928, Bd 27, N 4, 565-606 6. Karapetiants N.K. and Shankishvili L. D. A short proof of Hardy— Littlewood — Type theorem for fractional integrals in Holder spaces. Fractional Calculus and Applied Analysis. 1999. V. 2, № 2. P. 177-192.

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