Related papers: Critical heat kernel estimates via Hardy-Sobolev i…

On doubling metric measure spaces endowed with a strongly local regular Dirichlet form, we show some characterisations of pointwise upper bounds of the heat kernel in terms of global scale-invariant inequalities that correspond respectively…

We study the low-energy approximation for calculation of the heat kernel which is determined by the strong slowly varying background fields in strongly curved quasi-homogeneous manifolds. A new covariant algebraic approach, based on taking…

We show that the Lieb-Thirring inequalities on moments of negative eigenvalues of Schroedinger-like operators remain true, with possibly different constants, when the critical Hardy-weight $C|x|^{-2}$ is subtracted from the Laplace…

In this paper, we investigate cylindrical extensions of critical Sobolev type (improved Hardy) inequalities and identities in the style of Badiale-Tarantello [BT02], which in a special case give a critical Hardy inequality and its stability…

We investigate when the fundamental solution of the Schr\"odinger equation $\partial_t=\Delta+V$ posseses sharp Gaussian bounds global in space and time. We give a characterization for $V\leq 0$ and a sufficient condition for general $V$.

Let $L=-\Delta+V$ be a Schr\"odinger operator, where the potential $V$ belongs to the reverse H\"older class. By the subordinative formula, we introduce the fractional heat semigroup $\{e^{-t{L}^\alpha}\}_{t>0}, \alpha>0$, associated with…

We study strong ratio limit properties of the quotients of the heat kernels of subcritical and critical operators which are defined on a noncompact Riemannian manifold.

This paper studies Brownian motion and heat kernel measure on a class of infinite dimensional Lie groups. We prove a Cameron-Martin type quasi-invariance theorem for the heat kernel measure and give estimates on the $L^p$ norms of the…

We study the relationship between functional inequalities for a Markov kernel on a metric space $X$ and inequalities of transportation distances on the space of probability measures $\mathcal{P}(X)$. Extending results of Luise and Savar\'e…

The heat kernel expansion for a general non--minimal operator on the spaces $C^\infty (\Lambda^k)$ and $C^\infty (\Lambda^{p,q})$ is studied. The coefficients of the heat kernel asymptotics for this operator are expressed in terms of the…

We construct and estimate the fundamental solution of highly anisotropic space-inhomogeneous integro-differential operators. We use the Levi method. We give applications to the Cauchy problem for such operators.

We investigate Sobolev inequalities for several rough operators. We prove that several operators satisfy a pointwise bound by the Riesz potential applied to the gradient. From this inequality, we derive several new Sobolev-type inequalities…

Nash and Sobolev inequalities are known to be equivalent to ultracontractive properties of heat-like Markov semigroups, hence to uniform on-diagonal bounds on their kernel densities. In non ultracontractive settings, such bounds can not…

We study the heat semigroup generated by two-dimensional Schroedinger operators with compactly supported magnetic field. We show that if the field is radial, then the large time behavior of the associated heat kernel is determined by its…

We prove uniform Sobolev estimates for the resolvent of Schr\"odinger operators with large scaling-critical potentials without any repulsive condition. As applications, global-in-time Strichartz estimates including some non-admissible…

We study Sobolev and BV spaces on local trees which are metric spaces locally isometric to real trees. Such spaces are equipped with a Radon measure satisfying a locally uniform volume growth condition. Using the intrinsic geodesic…

In this paper, we prove the equivalent of ultracontractive bound of heat semigroup or the uniform upper bound of the heat kernel with the Nash inequality, Log-Sobolev inequalities on graphs. We also show that under the assumption of volume…

We consider a class of homogeneous partial differential operators on a finite-dimensional vector space and study their associated heat kernels. The heat kernels for this general class of operators are seen to arise naturally as the limiting…

In this paper we prove a sharp defective log-Sobolev inequality on H-type groups. Then we use such an inequality to show exponential integrability of Lipschitz functions with respect to the heat kernel measure. A defective log-Sobolev-type…

Let $H:=-\Delta+V$ be a nonnegative Schr\"odinger operator on $L^2({\bf R}^N)$, where $N\ge 2$ and $V$ is a radially symmetric function decaying quadratically at the space infinity. In this paper we consider the Schr\"odinger heat semigroup…