Pointwise Variable Anisotropic Function Spaces on Rn

Spaces of homogeneous type were introduced as a generalization to the Euclidean space and serve as a sufficient setting in which one can generalize the classical isotropic Harmonic analysis and function space theory. This setting is sometimes too general, and the theory is limited. Here, we present a set of flexible ellipsoid covers of ℝn that replace the Euclidean balls and support a generalization of the theory with fewer limitations.