PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2013 | 1 | 276-294
Tytuł artykułu

Resistance Conditions and Applications

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper studies analytic aspects of so-called resistance conditions on metric measure spaces with a doubling measure. These conditions are weaker than the usually assumed Poincaré inequality, but however, they are sufficiently strong to imply several useful results in analysis on metric measure spaces. We show that under a perimeter resistance condition, the capacity of order one and the Hausdorff content of codimension one are comparable. Moreover, we have connections to the Sobolev inequality for compactly supported Lipschitz functions on balls as well as capacitary strong type estimates for the Hardy-Littlewood maximal function. We also consider extensions to Sobolev type inequalities with two different measures and Lorentz type estimates.
Wydawca
Rocznik
Tom
1
Strony
276-294
Opis fizyczny
Daty
otrzymano
2013-03-28
zaakceptowano
2013-10-04
online
2013-10-25
Twórcy
Bibliografia
  • [1] M. T. Barlow, R. F. Bass and T. Kumagai, Stability of parabolic Harnack inequalities on metric measure spaces, J.Math. Soc. Japan 58 (2006), no. 2, 485–519.
  • [2] C. Bennett and S. Sharpley, Interpolation of Operators, Pure and Applied Mathematics, 129. Academic Press, Inc.,Boston, MA, 1988.
  • [3] A. Björn and J. Björn, Nonlinear Potential Theory on Metric Spaces, Tracts in Mathematics 17, European MathematicalSociety, 2011.
  • [4] Yu. A. Brudnyi and N. Ya. Krugljak, Interpolation functors and interpolation spaces, Vol. I. North-Holland MathematicalLibrary, 47. North-Holland Publishing Co., Amsterdam, 1991.
  • [5] J. Cerdà, Lorentz capacity spaces, Interpolation theory and applications, Contemp. Math. 445, 45–59, Amer. Math.Soc., Providence, RI, 2007.
  • [6] J. Cerdà, J. Martín and P. Silvestre, Capacitary function spaces, Collectanea Math. 62 (2011), no. 1, 95–118.
  • [7] J. Cerdà, J. Martín and P. Silvestre, Conductor Sobolev type estimates and isocapacitary inequalities, to appear inIndiana Univ. Math. J.
  • [8] S. Costea and V. G. Maz’ya, Conductor inequalities and criteria for Sobolev-Lorentz two-weight inequalities, Sobolevspaces in mathematics. II, 103–121, Int. Math. Ser. (N. Y.) 9 (2009), Springer, New York.
  • [9] A. Grigor’yan and A. Telcs, Harnack inequalities and sub-Gaussian estimates for random walks, Math. Ann. 324(2002), no. 3, 521–556.
  • [10] H. Hakkarainen and J. Kinnunen, The BV-capacity in metric spaces, Manuscripta Math. 132 (2010), no. 1-2, 51–73.
  • [11] H. Hakkarainen and N. Shanmugalingam, Comparisons of relative BV-capacities and Sobolev capacity in metricspaces, Nonlinear Anal. 74 (2011), no. 16, 5525–5543.
  • [12] J. Kinnunen, R. Korte, N. Shanmugalingam and H. Tuominen, Lebesgue points and capacities via boxing inequalityin metric spaces, Indiana Univ. Math. J. 57 (2008), no. 1, 401–430.[WoS]
  • [13] J. Kinnunen, R. Korte, N. Shanmugalingam and H. Tuominen, The DeGiorgi measure and an obstacle problemrelated to minimal surfaces in metric spaces, J. Math. Pures Appl. (9) 93 (2010), no. 6, 599–622.[WoS]
  • [14] V. G. Maz’ya, Conductor and capacitary inequalities for functions on topological spaces and their applications toSobolev type imbeddings, J. Funct. Anal. 224 (2005), no. 2, 408–430.
  • [15] V. G. Maz’ya, Conductor inequalities and criteria for Sobolev type two-weight imbeddings. J. Comput. Appl. Math.194 (2006), no. 11, 94–114.
  • [16] M. Miranda, Functions of bounded variation on "good" metric spaces, J. Math. Pures Appl. (9) 82 (2003), no. 8,975–1004.
  • [17] J. Orobitg and J. Verdera, Choquet integrals, Hausdorff content and the Hardy-Littlewood maximal operator, Bull.London Math. Soc. 30 (1998), no. 2, 145–150.
  • [18] P. Silvestre, Capacitary function spaces and applications, PhD-thesis (2012), TDR, B. 8121-2012.www.tesisenred.net/handle/10803/77717
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_agms-2013-0007
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.