# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Cauchy and Poisson integrals of ultradistributions. (English) Zbl 0712.46018

The authors define and study the generalized Cauchy and Poisson integrals of ultradistributions of Beurling type $𝒟\left(\left({M}_{p}\right),{L}^{s}\right)$ and of Roumieu type $𝒟\left(\left\{{M}_{p}\right\},{L}^{s}\right)$ both of which generalize Schwartz distributions ${𝒟}_{L}^{\text{'}}$ 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.

Reviewer: G.L.N.Rao
##### 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 ${ℂ}^{n}$ (Reinhardt, Hartogs, circular, tube) 32A10 Holomorphic functions (several variables) 32A40 Boundary behavior of holomorphic functions (several variables)