Related papers: Quaternionic spherical harmonics and a sharp multi…

Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and…

We prove a sharp integral gradient estimate for harmonic functions on noncompact K\"ahler manifolds. As application, we obtain a sharp estimate for the bottom of spectrum of the p-Laplacian and prove a splitting theorem for manifolds…

We present new sharp assertions concerning multipliers in various spaces of harmonic functions in the unit ball of $R^n$

We consider $L^p$-$L^q$ estimates for the spherical harmonic projection operators and obtain sharp bounds on a certain range of $p$, $q$. As an application, we provide a proof of off-diagonal Carleman estimates for the Laplacian, which…

On any quaternionic manifold of dimension greater than 4 a class of plurisubharmonic functions (or, rather, sections of an appropriate line bundle) is introduced. Then a Monge-Amp\`ere operator is defined. It is shown that it satisfies a…

We prove that, if \Delta_1 is the Hodge Laplacian acting on differential 1-forms on the (2n+1)-dimensional Heisenberg group, and if m is a Mihlin-H\"ormander multiplier on the positive half-line, with L^2-order of smoothness greater than…

Quaternionic and octonionic spinors are introduced and their fundamental properties (such as the space-times supporting them) are reviewed. The conditions for the existence of their associated Dirac equations are analyzed. Quaternionic and…

We prove a four dimensional version of the Bernstein Theorem, with complex polynomials being replaced by quaternionic polynomials. We deduce from the theorem a quaternionic Bernstein's inequality and give a formulation of this last result…

The main technical result of the paper is a Bochner type formula for the sub-laplacian on a quaternionic contact manifold. With the help of this formula we establish a version of Lichnerowicz' theorem giving a lower bound of the eigenvalues…

We establish endpoint estimates for a class of oscillating spectral multipliers on Lie groups of Heisenberg type. The analysis follows an earlier argument due to the second and fourth author but requires the detailed analysis of the wave…

In this paper we extend classical Titchmarsh theorems on the Fourier transform of H$\ddot{\text{o}}$lder-Lipschitz functions to the setting of harmonic $NA$ groups, which relate smoothness properties of functions to the growth and…

We completely describe spaces of multipliers of certain harmonic function spaces of Bergman type in R^n.This is the first sharp result of this kind for Bergman type mixed norm spaces of harmonic functions in the unit ball of R^n

In this article we prove an upper bound for a Hilbert polynomial on quaternionic Kaehler manifolds of positive scalar curvature. As corollaries we obtain bounds on the quaternionic volume and the degree of the associated twistor space.…

Let $X$ be a space of homogeneous type and let $L$ be an injective, non-negative, self-adjoint operator on $L^2(X)$ such that the semigroup generated by $-L$ fulfills Davies-Gaffney estimates of arbitrary order. We prove that the operator…

In a recent work, P. Chen and E. M. Ouhabaz proved a $p$-specific $L^p$-spectral multiplier theorem for the Grushin operator acting on $\mathbb{R}^{d_1}\times\mathbb{R}^{d_2}$ which is given by \[ L =-\sum_{j=1}^{d_1} \partial_{x_j}^2 -…

In this paper we prove Lp multiplier theorems for invariant and non-invariant operators on compact Lie groups in the spirit of the well-known Hormander-Mikhlin theorem on Rn and its variants on tori Tn. We also give applications to a-priori…

We prove the equivalence of several natural notions of conformal maps between sub-Riemannian manifolds. Our main contribution is in the setting of those manifolds that support a suitable regularity theory for subelliptic $p$-Laplacian…

In this paper we investigate the Brolin's theorem over $\mathbb{H}$, the skew field of quaternions. Moreover, considering a quaternionic polynomial $p$ with real coefficients, we focus on the properties of its equilibrium measure, among the…

Hormander-Mihklin type multiplier theorem on compacts manifolds withour boundary has been obtained by using the wave kernels. We consider maximal multiplies on this setting. To obtain the result, we carefully deal with the remainder terms…

We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms…