| 摘要: | 摘要： Triebel (J Approx Theory 35:275–297, 1982 ; 52:162–203, 1988 ) investigated the boundary values of the harmonic functions in spaces of the Triebel–Lizorkin type F p α , q on R + n + 1 by finding an characterization of the homogeneous Triebel–Lizorkin space F ˙ p α , q via its harmonic extension, where 0 < p < ∞ , 0 < q ≤ ∞ , and α < min { - n / p , - n / q } . In this article, we extend Triebel’s result to α < 0 and 0 < p , q ≤ ∞ by using a discrete version of reproducing formula and discretizing the norms in both F p α , q and F ˙ p α , q . Furthermore, for α < 0 and 1 < p , q ≤ ∞ , the mapping from harmonic functions in F p α , q to their boundary values forms a topological isomorphism between F p α , q and F ˙ p α , q .
其他題名： Integr. Equ. Oper. Theory
出版者： Basel: Springer Basel
出版日期： 2014-05-01
出處： Integral equations and operator theory, 2014-05, Vol.79 (1), p.23-48
資源來源： SpringerLink Journals
版權： Springer Basel 2014
識別號： ISSN: 0378-620X
識別號： EISSN: 1420-8989
識別號： DOI: 10.1007/s00020-014-2137-x |
