We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.

We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.

In this study, sharp rearrangement inequalities for the fractional Bmaximal function Mα,γf are obtained in the Lorentz spaces Lp,q,γ and by using these inequalities the boundedness conditions of the operator Mα,γ are found. Then, the conditions for the boundedness of the Bmaximal operator Mγ are obtained in Lp,q,γ .

Abstract We discuss when an operator T, subject to a rather general inequality in hereditary form, admits unitarily equivalent functional model of Agler type the reproducing kernel Hilbert space associated inequality. The need not be Nevanlinna-Pick type. define defect D our context and structure spectrum T is finite rank. As second application, some consequences concerning ergodic behavior are...