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Sharp constants in hardy type inequalities

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Abstract

We prove new weighted Hardy type inequalities with sharp constants and describe their applications to inequalities in multidimensional domains.

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References

  1. Davies, E. B. “The Hardy Constant,” Quart. J.Math. Oxford (2) 46, No. 4, 417–431 (1995).

    Article  MATH  Google Scholar 

  2. Matskewich, T., Sobolevskii, P. E. “The Best Possible Constant in a Generalized Hardy’s Inequality for Convex Domains in Rn,” Nonlinear Anal. 28, 1601–1610 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  3. Marcus, M., Mitzel, V. J., Pinchover, Y. “On the Best Constant for Hardy’s Inequality in Rn,” Trans. Amer. Math. Soc. 350, 3237–3250 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  4. Miklyukov, V. M., Vuorinen, M. R. “Hardy’s Inequality for W 1,p0 -Functions on RiemannianManifolds,” Proc. Amer.Math. Soc. 127, No. 9, 2145–2154 (1999).

    Article  MathSciNet  Google Scholar 

  5. Barbatis, G., Filippas, S., Tertikas, A. “A Unified Approach to Improved Lp Hardy Inequalities with Best Constants,” Trans. Amer.Math. Soc. 356, No. 6, 2169–2196 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  6. Avkhadiev, F. G., Wirths, K.-J. “Unified Poincaréand Hardy Inequalities with Sharp Constants for Convex Domains,” Z. Angew.Math. Mech. 87, No. 8–9, 632–642 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  7. Avkhadiev, F. G., Wirths, K.-J. “Sharp Hardy-Type Inequalities with Lamb’s Constants,” Bull. Belg. Math. Soc. Simon Stevin 18, 723–736 (2011).

    MathSciNet  MATH  Google Scholar 

  8. Avkhadiev, F. G. “Hardy Type Inequalities in Higher Dimensions with Explicit Estimate of Constants,” Lobachevskii J.Math. 21, 3–31 (2006).

    MathSciNet  MATH  Google Scholar 

  9. Avkhadiev F.G. “Hardy-Type Inequalities on Planar and Spatial Open Sets,” Proc. Steklov Inst.Math. 255, 2–12 (2006). 255 (1), 2–12 (2006).

    Article  MathSciNet  Google Scholar 

  10. Avkhadiev, F.G., Shafigullin, I. K. “Sharp Estimates of Hardy Constants for Domains with Special Boundary Properties,” Russian Mathematics (Iz. VUZ) 58, No. 2, 58–61 (2014).

    MathSciNet  MATH  Google Scholar 

  11. Avkhadiev, F.G., Laptev, A. “Hardy Inequalities for Nonconvex Somains,” InternationalMathematical Series “Around Research of Vladimir Maz’ya, I”. Function Spaces, Springer, Vol. 11, 1–12 (2010).

    MathSciNet  Google Scholar 

  12. Avkhadiev, F.G. “Families of Domains with Best PossibleHardy Constant,” RussianMathematics (Iz.VUZ) 57, No. 9, 49–52 (2013).

    MathSciNet  MATH  Google Scholar 

  13. Avkhadiev, F. G. “A Geometric Description of Domains Whose Hardy Constant is Equal to 1/4,” Izv. Math. 78, No. 5, 855–876 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  14. Avkhadiev, F. G. “Hardy Type L p -Inequalities in r-Close-to-Convex Domains,” Russian Mathematics (Iz. VUZ) 59, No. 1, 71–74 (2015).

    MathSciNet  Google Scholar 

  15. Prokhorov, D. V., Stepanov, V. D. “Weighted Estimates for the Riemann-Liouville Operators and Applications,” Proc. Steklov Inst.Math. 243, 278–301 (2003).

    MathSciNet  Google Scholar 

  16. Polovinkin, E. S., Balashov, M. V. Elements of Convex and Strongly Convex Analysis (Fizmatlit, Moscow, 2004) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    F. G. Avkhadiev

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  1. F. G. Avkhadiev
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Correspondence to F. G. Avkhadiev.

Additional information

Original Russian Text © F.G. Avkhadiev, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 10, pp. 61–65.

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Avkhadiev, F.G. Sharp constants in hardy type inequalities. Russ Math. 59, 53–56 (2015). https://doi.org/10.3103/S1066369X15100060

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  • DOI: https://doi.org/10.3103/S1066369X15100060

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