Local Hardy Spaces Associated With Ellipsoid Covers And The Boundedness Of The Related Pseudo-differential Operators

In 2010,Dekel et al.introduced a multi-level ellipsoid covers framework that are highly anisotropic in the sence that the ellipsoids can change shape rapidly from point to point and from level to level.We accomplied the following two things associated with ellipsoid covers.We first introduce a class of local Hardy spaces associated with ellipsoid covers and obtain its atomic decomposition and finite atomic decomposition.As application,we obtain some boundedness criterions for(sub)linear operators.Then we introduce a class of inhomogeneous pseudo-differential symbols class adapted to ellipsoid covers and obtain its boundedness on L2(Rn).