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Characterizations of bounded sets in spaces of ultradistributions. (English) Zbl 0816.46026
Summary: We characterize bounded sets in ultradistribution spaces \({\mathcal D}^{\prime(M_ p)}_{L^ t}\), \(t\in [1, \infty]\), \({\mathcal S}^{\prime\{M_ p\}}\), and \({\mathcal S}^{\prime(M_ p)}\) and bounded sets and convergent sequences in \({\mathcal D}^{\prime(M_ p)}\) and \({\mathcal D}^{\prime\{M_ p\}}\) via the convolution by corresponding test functions. The structural theorems for \({\mathcal D}^{\prime\{M_ p\}}_{L^ t}\) and \(\widetilde{\mathcal D}^{\prime\{M_ p\}}_{L^ t}\), \(t\in [1, \infty]\), are also given.

MSC:
46F05 Topological linear spaces of test functions, distributions and ultradistributions
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