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On an integral inequality and related summability results

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Abstract

We introduce the class E p q of functions satisfying a new integral reverse inequality and we study the relationships with the classical Gehring and Muckenhaupt classes. In our main result, we prove higher integrability properties that generalize and improve the results obtained in [7] and [1].

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References

  1. H. Alzer, An improvement of the constants in a reverse integral inequality, J. Math. Anal. Appl., 190(1995), 774–779.

    Google Scholar 

  2. B. Bojarski, C. Sbordone, and I. Wik, The Muckenhoupt class A 1(R), Studia Math., 101(1992), 155–163.

    Google Scholar 

  3. L. D'Apuzzo and C. Sbordone, Reverse Hölder inequalities. A sharp result, Rend. Mat. VII, 10(1990), 357–366.

    Google Scholar 

  4. M. Franciosi and G. Moscariello, Higher integrability results, Manuscripta Math., 52(1985), 151–170.

    Google Scholar 

  5. A. A. Korenovskii, The exact continuation of a reverse Hölder inequality and Muckenhoupt condition, Math. Notes, 52(1992), 145–152.

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

    Google Scholar 

  7. L. Nania, On some reverse integral inequalities, J. Austral. Math. Soc., 49(1990), 319–326.

    Google Scholar 

  8. A. Popoli, Optimal integrability in B q p classes, Le Matematiche, 52(1997), 159–170.

    Google Scholar 

  9. C. Sbordone, Higher integrability from reverse integral inequalities, Proc. Int. Meeting of Methods of Functional Analysis and Theory of Elliptic Equations, Napoli, Liguori (1983), 347–357.

  10. D. T. Shum, On integral inequalities related to Hardy's, Canad. Math. Bull., 14(1971), 225–230.

    Google Scholar 

  11. I. Wik, Truncation of weight functions, Preprint (1992).

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Popoli, A. On an integral inequality and related summability results. Analysis Mathematica 29, 135–145 (2003). https://doi.org/10.1023/A:1023952410274

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