ACTA issues

Distributional boundary values of generalized Hardy functions in Beurling's tempered distributions

Byung Keun Sohn

Acta Sci. Math. (Szeged) 85:3-4(2019), 595-611

Abstract. Let $B$ be a proper open subset in \rn \ and $C$ be an open convex cone in \rn . We define a generalization of the spaces of Hardy functions, \gb , $1 \leq p < \infty ,$ and extended tempered distributions, \Swp , of Beurling's tempered distributions, \swp . We obtain the analytical and topological properties of \Swp \ and show that the functions in \gc , $1 < p \leq 2$, have distributional boundary values in the weak topology of \swp \ using the analytical properties of \Swp .

DOI: 10.14232/actasm-018-088-3

AMS Subject Classification (1991): 32A40, 42B30, 46F20

Keyword(s): Beurling distributions, generalized Hardy functions, distributional boundary values

Received October 7, 2018 and in final form January 13, 2019. (Registered under 88/2018.)