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Estimation of Equimeasurable Rearrangements in the Anisotropic Case

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Ukrainian Mathematical Journal Aims and scope

We study the classes of functions satisfying the reverse Hölder inequality on segments in the multidimensional case. For these classes, we obtain sharp estimates of the “norms” of equimeasurable rearrangements.

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References

  1. G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press, Cambridge (1934).

    MATH  Google Scholar 

  2. E. H. Lieb and M. Loss, Analysis [Russian translation], Nauchnaya Kniga, Novosibirsk (1998).

    MATH  Google Scholar 

  3. B. Muckenhoupt, “Weighted norm inequalities for the Hardy maximal function,” Trans. Amer. Math. Soc., 165, 207–226 (1972).

    Article  MathSciNet  Google Scholar 

  4. F. W. Gehring, “The L p-integrability of the partial derivatives of a quasiconformal mapping,” Acta Math., 130, No. 1, 265–277 (1973).

    Article  MathSciNet  Google Scholar 

  5. C. L. Fefferman and E. M. Stein, “H p spaces of several variables,” Acta Math., 129, 137–193 (1972).

    Article  MathSciNet  Google Scholar 

  6. F. John and L. Nirenberg, “On functions of bounded mean oscillation,” Comm. Pure Appl. Math., 14, Issue 3, 415–426 (1961).

    Article  MathSciNet  Google Scholar 

  7. A. A. Korenovskii, Mean Oscillations and Equimeasurable Rearrangements of Functions, Springer, Berlin (2007).

    Book  Google Scholar 

  8. C. Sbordone, “Rearrangement of functions and reverse Jensen inequalities,” Proc. Sympos. Pure Math., 45, Pt II, 325–329 (1986).

  9. A. A. Korenovskii, “On the exact extension of the reverse Hölder inequality and Muckenhoupt conditions,” Mat. Zametki, 52, Issue 6, 32–44 (1992).

  10. A. Fiorenza, “BMO regularity for one-dimensional minimizers of some Lagrange problems,” J. Convex Anal., 4, No. 2, 289–303 (1997).

    MathSciNet  MATH  Google Scholar 

  11. R. Shanin, “Equimeasurable rearrangements of functions satisfying the reverse Hölder or the reverse Jensen inequality,” Ric. Mat., 64, 217–228 (2015).

    Article  MathSciNet  Google Scholar 

  12. R. V. Shanin, “On the reverse Hölder and Jensen inequalities,” Visn. Odes. Nats. Univ., Mat. Mekh., 17, Issue 3(15), 60–67 (2012).

  13. A. A. Korenovskyy, A. K. Lerner, and A. M. Stokolos, “On a multidimensional form of F. Riesz ‘rising sun’ lemma,” Proc. Amer. Math. Soc., 133, No. 5, 1437–1440 (2005).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Economics, and Mechanics, Mechnikov Odessa National University, Odessa, Ukraine

    R. V. Shanin

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  1. R. V. Shanin
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 7, pp. 968–977, July, 2018.

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Shanin, R.V. Estimation of Equimeasurable Rearrangements in the Anisotropic Case. Ukr Math J 70, 1115–1126 (2018). https://doi.org/10.1007/s11253-018-1555-3

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  • DOI: https://doi.org/10.1007/s11253-018-1555-3

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