Characterizations of bounded sets in spaces of ultradistributions

Abstract:

We characterize bounded sets in ultradistributions spaces $\mathcal {D}_{{L^t}}^{’({M_p})}, t \in [1,\infty ], S{’^{\{ {M_p}\} }}$, and $S{’^{({M_p})}}$ and bounded sets and convergent sequences in $\mathcal {D}{’^{({M_p})}}$ and $\mathcal {D}{’^{\{ {M_p}\} }}$ via the convolution by corresponding test functions. The structural theorems for $\mathcal {D}_{{L^t}}^{’\{ {M_p}\} }$ and $\widetilde D_{{L^t}}^{’\{ {M_p}\} },\;t \in [1,\infty ]$, are also given.