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Izv. Vyssh. Uchebn. Zaved. Mat., 2011, Number 9, Pages 90–94 (Mi ivm7933)  

This article is cited in 11 scientific papers (total in 11 papers)

Brief communications

Hardy-type inequalities with power and logarithmic weights in domains of the Euclidean space

F. G. Avkhadiev, R. G. Nasibullin, I. K. Shafigullin

Chair of Function Theory and Approximations, Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: We consider Hardy-type inequalities in domains of the Euclidean space for the case, when the weight depends on the distance function to the domain boundary and has power and logarithmic singularities. We prove several new inequalities with sharp constants.

Keywords: Hardy-type inequalities, distance function to the boundary, iterations of logarithms.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:9, 76–79

Bibliographic databases:

Document Type: Article
UDC: 517.5+517.956
Received: 28.02.2011

Citation: F. G. Avkhadiev, R. G. Nasibullin, I. K. Shafigullin, “Hardy-type inequalities with power and logarithmic weights in domains of the Euclidean space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 9, 90–94; Russian Math. (Iz. VUZ), 55:9 (2011), 76–79

Citation in format AMSBIB
\by F.~G.~Avkhadiev, R.~G.~Nasibullin, I.~K.~Shafigullin
\paper Hardy-type inequalities with power and logarithmic weights in domains of the Euclidean space
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 9
\pages 90--94
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 9
\pages 76--79

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    This publication is cited in the following articles:
    1. F. G. Avkhadiev, “Families of domains with best possible Hardy constant”, Russian Math. (Iz. VUZ), 57:9 (2013), 49–52  mathnet  crossref  zmath
    2. F. G. Avkhadiev, I. K. Shafigullin, “Otsenki konstant Khardi pri trubchatom rasshirenii mnozhestv i v oblastyakh s konechnymi granichnymi momentami”, Matem. tr., 16:2 (2013), 3–12  mathnet  mathscinet; F. G. Avkhadiev, I. K. Shafigullin, “Estimates of Hardy's constants for tubular extensions of sets and domains with finite boundary moments”, Siberian Adv. Math., 24:3 (2014), 153–158  crossref
    3. R. G. Nasibullin, A. M. Tukhvatullina, “Hardy type inequalities with logarithmic and power weights for a special family of non-convex domains”, Ufa Math. Journal, 5:2 (2013), 43–55  mathnet  crossref  mathscinet  elib
    4. R. G. Nasibullin, “Tochnost konstant logarifmicheskikh neravenstv tipa Khardi v otkrytykh mnogomernykh oblastyakh”, Fiziko-matematicheskie nauki, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 155, no. 3, Izd-vo Kazanskogo un-ta, Kazan, 2013, 111–125  mathnet
    5. R. G. Nasibullin, “Generalizations of Hardy-Type Inequalities in the Form of Dubinskii”, Math. Notes, 95:1 (2014), 98–110  mathnet  crossref  crossref  isi  elib  elib
    6. F. G. Avkhadiev, R. G. Nasibullin, “Hardy-type inequalities in arbitrary domains with finite inner radius”, Siberian Math. J., 55:2 (2014), 191–200  mathnet  crossref  mathscinet  isi
    7. F. G. Avkhadiev, “A geometric description of domains whose Hardy constant is equal to 1/4”, Izv. Math., 78:5 (2014), 855–876  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. R. G. Nasibullin, “Ob odnom diskretnom neravenstve tipa Khardi s logarifmicheskim vesom”, Vladikavk. matem. zhurn., 18:2 (2016), 67–75  mathnet
    9. Nasibullin R., “Hardy Type Inequalities With Weights Dependent on the Bessel Functions”, Lobachevskii J. Math., 37:3 (2016), 274–283  crossref  isi
    10. R. G. Nasibullin, “Sharp Hardy type inequalities with weights depending on Bessel function”, Ufa Math. Journal, 9:1 (2017), 89–97  mathnet  crossref  elib
    11. I. K. Shafigullin, “Lower bound for the Hardy constant for an arbitrary domain in $\mathbb{R}^n$”, Ufa Math. Journal, 9:2 (2017), 102–108  mathnet  crossref  elib
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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