8 papers
Lieb-Thirring inequalities for the Dirac operator on spheres
Uwe Kähler, André Pedroso Kowacs, Michael Ruzhansky
In this paper, we obtain bounds for the best constants in two inequalities which can be seen as analogues of the Lieb-Thirring inequality, but with the Dirac operator, on the s…
A Fourier analysis for -periodic functions and applications
André Pedroso Kowacs, Marielle Aparecida Silva
We develop a Fourier analysis for a generalization of the class of periodic functions, often referred to as -periodic functions, and prove several properties and inequalit…
Global Hypoellipticity and Solvability with Loss of Derivatives on the Torus
André Pedroso Kowacs, Alexandre Kirilov
This paper provides a complete characterization of global hypoellipticity and solvability with loss of derivatives for Fourier multiplier operators on the -dimensional torus. We…
Directional Poincaré inequality on compact Lie groups
Paulo L. Dattori da Silva, André Pedroso Kowacs
We extend the directional Poincaré inequality on the torus, introduced by Steinerberger in [Ark. Mat. 54 (2016), pp. 555--569], to the setting of compact Lie groups. We provide ne…
Global hypoellipticity of systems of Fourier multipliers on compact Lie groups
André Pedroso Kowacs
We apply the characterization of global hypoellipticity for -invariant operators on homogeneous vector bundles obtained by Cardona and Kowacs [J. Pseudo-Differ. Oper. Appl. 16,…
On the Sobolev boundedness of vector fields on compact Riemannian manifolds
Duván Cardona, Alexandre Kirilov, Wagner A. A. de Moraes +1
We analyze the sharpness of the Sobolev order for left-invariant vector fields on compact Riemannian manifolds. Utilizing techniques from pseudo-differential operator theory and mi…