Affiliation:
1. Department of Mathematics, Wake Forest University, Winston-Salem, NC 27109-7388, USA
Abstract
Vector-valued analytic functions in Cn, which are known to have vector-valued tempered distributional boundary values, are shown to be in the Hardy space Hp,1≤p<2, if the boundary value is in the vector-valued Lp,1≤p<2, functions. The analysis of this paper extends the analysis of a previous paper that considered the cases for 2≤p≤∞. Thus, with the addition of the results of this paper, the considered problems are proved for all p,1≤p≤∞.
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference18 articles.
1. Streater, R.F., and Wightman, A.S. (1964). PCT, Spin and Statistics, and All That, W.A. Benjamin, Inc.
2. Simon, B. (1974). The P(Φ)2 Euclidean (Quantum)Field Theory, Princeton University Press.
3. On the role of Hardy spaces in form factor bounds;Raina;Lett. Math. Phys.,1978
4. Holomorphic functions in tubes which have distributional boundary values and which are Hp functions;Carmichael;SIAM J. Math. Anal.,1983
5. Vector-valued Hardy spaces related to analytic functions having distributional boundary values;Carmichael;Complex Var. Ellip. Equ.,2019