On Tempered Ultradistributions in Classical Morrey Spaces

Abstract

We introduce the notion of tempered ultradistributions in classical Morrey spaces by preserving their respective properties. Moreover we investigate some embedding results within the scale of classical Morrey spaces (local Morrey space $\mathcal{L}^{p,\beta}(\mathbb{C}^{n},\mu)$ or global Morrey space $L^{p,\beta}(\mathbb{C}^{n})$ where the underlying functions $\mu$ satisfy the growth condition by polxnomials. Finally we present some results on the new classical Morrey spaces described by tempered ultradistributions satisfying both the vanishing and slow growth conditions in form of embedding theorems.