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Moduli of continuity and rearrangements

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Abstract

It is proved that the modulus of continuity of a function in Lp(0, 1) majorizes the modulus of continuity of its decreasing rearrangement.

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Literature cited

  1. A. Zygmund, Trigonometric Series, Vol. 1, Cambridge University Press, Cambridge (1959).

    Google Scholar 

  2. P. L. Ul'yanov, “Imbedding of certain functions in H ωp ” Izv. Akad. Nauk SSSR, Ser. Matem.,32, 649–686 (1968).

    Google Scholar 

  3. E. A. Storozhenko, “Necessary and sufficient conditions for imbedding certain classes of functions,” Izv. Akad. Nauk SSSR Ser. Matem.,37, 386–398 (1973).

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  4. K. I. Oskolkov and S. A. Telyakovskii, “P. L. Ul'yanov's estimates for integral moduli of continuity,” Izv. Akad. Nauk ArmSSR, Matematika,6, No. 5, 406–411 (1971).

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  5. G. D. Mostow, “Quasiconformal maps in n-space and the rigidity of hyperbolic space forms,” Publ. Inst. Math. (Beograd),34, 53–104 (1968).

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  6. G. Pólya and G. Szegö, Isoperimatric Inequalities in Mathematical Physics, Princeton University Press, Princeton (1951).

    Google Scholar 

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Authors and Affiliations

  1. Dnepropetrovskii Chemico-Technological Institute, USSR

    Yu. A. Brudnyi

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  1. Yu. A. Brudnyi
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Translated from Matematicheskii Zametki, Vol. 18, No. 1, pp. 63–66, July, 1975.

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Brudnyi, Y.A. Moduli of continuity and rearrangements. Mathematical Notes of the Academy of Sciences of the USSR 18, 619–621 (1975). https://doi.org/10.1007/BF01461142

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  • DOI: https://doi.org/10.1007/BF01461142

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