*(English)*Zbl 0712.46018

The authors define and study the generalized Cauchy and Poisson integrals of ultradistributions of Beurling type $\mathcal{D}(\left({M}_{p}\right),{L}^{s})$ and of Roumieu type $\mathcal{D}(\left\{{M}_{p}\right\},{L}^{s})$ both of which generalize Schwartz distributions ${\mathcal{D}}_{L}^{\text{'}}$ for appropriate values of s. Thirteen theorems have been proved in this convection.

The authors claim that the work contained in the paper under review, may form a foundation for future research concerning a study of holomorphic functions in tubes which are characterised by either pointwise or norm growths, their boundary values, their recovery in terms of generalized integrals including some related properties. A detailed account of the lines on which this can be accomplished, is also given at the end of the paper.

##### MSC:

46F12 | Integral transforms in distribution spaces |

46F15 | Hyperfunctions, analytic functionals |

46F20 | Distributions and ultradistributions as boundary values of analytic functions |

32A07 | Special domains in ${\u2102}^{n}$ (Reinhardt, Hartogs, circular, tube) |

32A10 | Holomorphic functions (several variables) |

32A40 | Boundary behavior of holomorphic functions (several variables) |