Gradient estimates for heat kernels and harmonic functions
Coulhon, T., Jiang, R., Koskela, P., & Sikora, A. (2020). Gradient estimates for heat kernels and harmonic functions. Journal of Functional Analysis, 278(8), Article 108398. https://doi.org/10.1016/j.jfa.2019.108398
Julkaistu sarjassa
Journal of Functional AnalysisPäivämäärä
2020Tekijänoikeudet
© 2019 Elsevier Inc.
Let (X,d,μ) be a doubling metric measure space endowed with a Dirichlet form E deriving from a “carré du champ”. Assume that (X,d,μ,E) supports a scale-invariant L2-Poincaré inequality. In this article, we study the following properties of harmonic functions, heat kernels and Riesz transforms for p∈(2,∞]:
(i) (Gp): Lp-estimate for the gradient of the associated heat semigroup;
(ii) (RHp): Lp-reverse Hölder inequality for the gradients of harmonic functions;
(iii) (Rp): Lp-boundedness of the Riesz transform (p<∞);
(iv) (GBE): a generalised Bakry-Émery condition.
We show that, for p∈(2,∞), (i), (ii) (iii) are equivalent, while for p=∞, (i), (ii), (iv) are equivalent. Moreover, some of these equivalences still hold under weaker conditions than the L2-Poincaré inequality.
Our result gives a characterisation of Li-Yau's gradient estimate of heat kernels for p=∞, while for p∈(2,∞) it is a substantial improvement as well as a generalisation of earlier results by Auscher-Coulhon-Duong-Hofmann [7] and Auscher-Coulhon [6]. Applications to isoperimetric inequalities and Sobolev inequalities are given. Our results apply to Riemannian and sub-Riemannian manifolds as well as to non-smooth spaces, and to degenerate elliptic/parabolic equations in these settings.
...
Julkaisija
ElsevierISSN Hae Julkaisufoorumista
0022-1236Asiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/33599622
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Rahoittaja(t)
Suomen AkatemiaRahoitusohjelmat(t)
Huippuyksikkörahoitus, SALisätietoja rahoituksesta
T. Coulhon and A. Sikora were partially supported by Australian Research Council Discovery grant DP130101302. This research was undertaken while T. Coulhon was employed by the Australian National University. R. Jiang was partially supported by NNSF of China (11922114 & 11671039), P. Koskela was partially supported by the Academy of Finland via the Centre of Excellence in Analysis and Dynamics Research (project No. 307333). ...Lisenssi
Samankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
Riesz transform and vertical oscillation in the Heisenberg group
Fässler, Katrin; Orponen, Tuomas (Mathematical Sciences Publishers, 2023)We study the L2-boundedness of the 3-dimensional (Heisenberg) Riesz transform on intrinsic Lipschitz graphs in the first Heisenberg group H. Inspired by the notion of vertical perimeter, recently defined and studied by ... -
Uniform rectifiability and ε-approximability of harmonic functions in Lp
Hofmann, Steve; Tapiola, Olli (Centre Mersenne; l'Institut Fourier,, 2020)Suppose that E⊂Rn+1 is a uniformly rectifiable set of codimension 1. We show that every harmonic function is ε-approximable in Lp(Ω) for every p∈(1,∞), where Ω:=Rn+1∖E. Together with results of many authors this shows that ... -
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 ... -
ε-approximability of harmonic functions in Lp implies uniform rectifiability
Bortz, Simon; Tapiola, Olli (American Mathematical Society, 2019) -
Polynomial and horizontally polynomial functions on Lie groups
Antonelli, Gioacchino; Le Donne, Enrico (Springer, 2022)We generalize both the notion of polynomial functions on Lie groups and the notion of horizontally affine maps on Carnot groups. We fix a subset S of the algebra g of left-invariant vector fields on a Lie group G and we ...
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.