Boundedness of Pseudodifferential Operators on Realized Homogeneous Besov Spaces

Abstract

Using the notion of realizations, the realized homogeneous Besov spaces $\dot{\widetilde{B}}{^{s}_{p,q}}(\mathbb{R}^n)$ are subsets of tempered distributions. Then we will study the boundedness of some pseudodifferential operators on $\dot{\widetilde{B}}{^{s}_{p,q}}(\mathbb{R}^n)$, in the cases either $s \lt n/p$ or $s = n/p$ and $q = 1$.