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We prove a family of Hardy-Rellich and Poincare identities and inequalities on the hyperbolic space having, as particular cases, improved Hardy-Rellich, Rellich and second order Poincare inequalities. All remainder terms provided considerably improve those already known in literature, and all identities hold with same constants for radial operators also. Furthermore, as applications of the main results, second ord
We prove infinite-dimensional second order Poincare inequalities on Wiener space, thus closing a circle of ideas linking limit theorems for functionals of Gaussian fields, Steins method and Malliavin calculus. We provide two applications: (i) to a ne
We establish sharp Hardy-Adams inequalities on hyperbolic space $mathbb{B}^{4}$ of dimension four. Namely, we will show that for any $alpha>0$ there exists a constant $C_{alpha}>0$ such that [ int_{mathbb{B}^{4}}(e^{32pi^{2} u^{2}}-1-32pi^{2} u^{2})d
We study the second order hyperbolic equations with initial conditions, a nonhomogeneous Dirichlet boundary condition and a source term. We prove the solution possesses $H^1$ regularity on any piecewise $C^1$-smooth non-timelike hypersurfaces. We gen
We propose and prove an identity relating the Poincare polynomials of stabilizer subgroups of the affine Weyl group and of the corresponding stabilizer subgroups of the Weyl group.
We prove Rellich and improved Rellich inequalities that involve the distance function from a hypersurface of codimension $k$, under a certain geometric assumption. In case the distance is taken from the boundary, that assumption is the convexity of t