Harmonic analysis associated to Schrödinger operator with Hardy potential

The purpose of this thesis is to study some properties associated to Schrödinger operator with Hardy potential La,a. The main results of this thesis are presented in three parts. The first part is dedicated to develop the Hardy and BMO spaces associated to La,a. We prove that our new function spaces enjoy some important results such as molecular decomposition. In the second part, the focus will be on the boundedness of variation operators, oscillation operators, and ?-jump operators associated to semigroup generated by La,a. In the third part, we study Besov spaces associated to La,a.