Related papers: Gradient estimates for the subelliptic heat kernel…

In this paper, we obtain a fractional Hardy inequality in the case $Q<sp$ on homogeneous Lie groups, and as an application we show the corresponding uncertainty principle. Also, we show a fractional Hardy-Sobolev type inequality on…

In the sub-Riemannian setting of Carnot groups, this work investigates a-priori estimates and Liouville type theorems for solutions of coercive, quasilinear differential inequalities of the type $$ \Delta_{\mathbb{G}}^\varphi u \ge b(x)…

Let $X$ be an abstract orientable not necessarily compact CR manifold of dimension $2n+1$, $n\geq1$, and let $L^k$ be the $k$-th tensor power of a CR complex line bundle $L$ over $X$. Suppose that condition $Y(q)$ holds at each point of…

We begin a systematic study of these spaces, initially following along the lines of Eberlein's comprehensive study of the Riemannian case. In particular, we integrate the geodesic equation, discuss the structure of the isometry group, and…

In this paper, we study elliptic gradient estimates for a nonlinear $f$-heat equation, which is related to the gradient Ricci soliton and the weighted log-Sobolev constant of smooth metric measure spaces. Precisely, we obtain Hamilton's and…

We give a direct proof of the sharp two-sided estimates, recently established in [4,9], for the Dirichlet heat kernel of the fractional Laplacian with gradient perturbation in $C^{1, 1}$ open sets by using Duhamel formula. We also obtain a…

We rederive the expression of the integrated density of states for \ the sub-Laplacian on Heisenberg groups $\mathbb{H}_{n}$ by using its resolvent kernel.

We provide general lower and upper bounds for Laplace Dirichlet heat kernel of convex $\mathcal C^{1,1}$ domains. The obtained estimates precisely describe the exponential behaviour of the kernels, which has been known only in a few special…

We prove certain gradient and eigenvalue estimates, as well as the heat kernel estimates, for the Hodge Laplacian on $(m,0)$ forms, i.e., sections of the canonical bundle of K\"ahler manifolds, where $m$ is the complex dimension of the…

In the first part of this paper, we get new Li-Yau type gradient estimates for positive solutions of heat equation on Riemmannian manifolds with $Ricci(M)\ge -k$, $k\in \mathbb R$. As applications, several parabolic Harnack inequalities are…

We prove that on an asymptotically Euclidean boundary groupoid, the heat kernel of the Laplacian is a smooth groupoid pseudo-differential operator.

In this paper, motivated by the works of Bakry et. al in finding sharp Li-Yau type gradient estimate for positive solutions of the heat equation on complete Riemannian manifolds with nonzero Ricci curvature lower bound, we first introduce a…

We give pointwise upper estimate for the gradient of the heat kernel on some fractal-like cable systems including the Vicsek and the Sierpi\'nski cable systems. Applications to $L^p$-boundedness of quasi-Riesz transforms are derived.

We study the behavior of the heat kernel of the Hodge Laplacian on a contact manifold endowed with a family of Riemannian metrics that blow-up the directions transverse to the contact distribution. We apply this to analyze the behavior of…

We study a generalization of the Bakry-\'Emery pointwise gradient estimate for the heat semigroup and its equivalence with some entropic inequalities along the heat flow and Wasserstein geodesics for metric-measure spaces with a suitable…

In sub-Riemannian geometry there exist, in general, no known explicit representations of the heat kernels, and these functions fail to have any symmetry whatsoever. In particular, they are not a function of the control distance, nor they…

We consider graph diffusion processes constructed from finite i.i.d. samples drawn from an unknown manifold embedded in ambient Euclidean space, where the graph affinity is defined by an ambient Gaussian kernel matrix. We show that the…

We make explicit the $p$-dependence of $C$ in the gradient estimate $\left\Vert \nabla u\right\Vert _{\infty}^{p-1}\leq C\left\Vert f\right\Vert _{N,1}$ by Cianchi and Maz'ya (2011). In such inequality, the constant $C$ is uniform with…

This article deals with a variation of constants type inequality for semigroups acting consistently on a scale of Banach spaces. This inequality can be characterized by a corresponding (easy to verify) inequality for their generators. The…

We consider the heat kernel (and the zeta function) associated with Laplace type operators acting on a general irreducible rank 1 locally symmetric space X. The set of Minakshisundaram- Pleijel coefficients {A_k(X)}_{k=0}^{\infty} in the…