Characterizations of bounded sets in spaces of ultradistributions

Abstract

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