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Elements of D'Lq (R) as boundary values of holomorphic functions

Skórnik U.

Demonstratio Mathematica

2000

Vol. 33, nr 3

657-663

In this paper we give a boundary value characterization of the space D'Lp(R) (see also [4]). Namely, we will show that every distribution that belongs to the space D'Lp(R) can be represented by analytic functions. We will also show that analytic functions fulfilling certain growth conditions have their boundary values in the space D'Lp (R). The characterization of holomorphic function spaces whose elements have boundary values in spaces of distributions and ultradistributions has a long history, see [2]-[6], [8] and [9].