Assouad Type Dimensions in Geometric Analysis
Lehrbäck, J. (2021). Assouad Type Dimensions in Geometric Analysis. In U. Freiberg, B. Hambly, M. Hinz, & S. Winter (Eds.), Fractal Geometry and Stochastics VI (pp. 25-46). Birkhäuser. Progress in Probability, 76. https://doi.org/10.1007/978-3-030-59649-1_2
Julkaistu sarjassa
Progress in ProbabilityTekijät
Päivämäärä
2021Oppiaine
MatematiikkaAnalyysin ja dynamiikan tutkimuksen huippuyksikköMathematicsAnalysis and Dynamics Research (Centre of Excellence)Tekijänoikeudet
© Springer Nature Switzerland AG 2021
We consider applications of the dual pair of the (upper) Assouad dimension and the lower (Assouad) dimension in analysis. We relate these notions to other dimensional conditions such as a Hausdorff content density condition and an integrability condition for the distance function. The latter condition leads to a characterization of the Muckenhoupt Ap properties of distance functions in terms of the (upper) Assouad dimension. It is also possible to give natural formulations for the validity of Hardy–Sobolev inequalities using these dual Assouad dimensions, and this helps to understand the previously observed dual nature of certain cases of these inequalities.
Julkaisija
BirkhäuserEmojulkaisun ISBN
978-3-030-59648-4Konferenssi
International Conference on Fractal Geometry and StochasticsKuuluu julkaisuun
Fractal Geometry and Stochastics VIISSN Hae Julkaisufoorumista
1050-6977Asiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/52590230
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Lisenssi
Samankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
A quantitative second order estimate for (weighted) p-harmonic functions in manifolds under curvature-dimension condition
Liu, Jiayin; Zhang, Shijin; Zhou, Yuan (Elsevier, 2024)We build up a quantitative second-order Sobolev estimate of lnw for positive p-harmonic functions w in Riemannian manifolds under Ricci curvature bounded from below and also for positive weighted p-harmonic functions w in ... -
The Hajłasz Capacity Density Condition is Self-improving
Canto, Javier; Vähäkangas, Antti V. (Springer Science and Business Media LLC, 2022)We prove a self-improvement property of a capacity density condition for a nonlocal Hajłasz gradient in complete geodesic spaces with a doubling measure. The proof relates the capacity density condition with boundary ... -
Loomis-Whitney inequalities in Heisenberg groups
Fässler, Katrin; Pinamonti, Andrea (Springer Science and Business Media LLC, 2022)This note concerns Loomis–Whitney inequalities in Heisenberg groups Hn: |K|≲∏j=12n|πj(K)|n+1n(2n+1), K⊂Hn. Here πj, j=1,…,2n, are the vertical Heisenberg projections to the hyperplanes {xj=0}, respectively, and |⋅| refers ... -
Magnetic fractional Poincaré inequality in punctured domains
Bal, Kaushik; Mohanta, Kaushik; Roy, Prosenjit (Elsevier, 2024)We study Poincaré-Wirtinger type inequalities in the framework of magnetic fractional Sobolev spaces. In the local case, Lieb et al. (2003) [19] showed that, if a bounded domain Ω is the union of two disjoint sets Γ and ... -
Stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds
Nobili, Francesco; Violo, Ivan Yuri (Elsevier, 2024)We study the qualitative stability of two classes of Sobolev inequalities on Riemannian manifolds. In the case of positive Ricci curvature, we prove that an almost extremal function for the sharp Sobolev inequality is close ...
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.