TY - JOUR

T1 - Boundary Values of Harmonic Functions in Spaces of Triebel-Lizorkin Type

AU - Lin, Chin Cheng

AU - Lin, Ying Chieh

N1 - Funding Information:
The authors are grateful to the referee for valuable comments. Research of C.-C. Lin and Y.-C. Lin was supported by NSC of Taiwan under Grant #NSC 100-2115-M-008-002-MY3 and #NSC 102-2115-M-008-001, respectively.

PY - 2014/5

Y1 - 2014/5

N2 - 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 Fα, qp on Rn+1+ by finding an characterization of the homogeneous Triebel-Lizorkin space Ḟα,qp 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 Ḟα,qp. Furthermore, for α < 0 and 1 < p,q ≤ ∞, the mapping from harmonic functions in Fα,qp to their boundary values forms a topological isomorphism between Fα,qp and Ḟα,qp.

AB - 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 Fα, qp on Rn+1+ by finding an characterization of the homogeneous Triebel-Lizorkin space Ḟα,qp 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 Ḟα,qp. Furthermore, for α < 0 and 1 < p,q ≤ ∞, the mapping from harmonic functions in Fα,qp to their boundary values forms a topological isomorphism between Fα,qp and Ḟα,qp.

KW - Boundary values

KW - harmonic functions

KW - Triebel-Lizorkin spaces

UR - http://www.scopus.com/inward/record.url?scp=84898905102&partnerID=8YFLogxK

U2 - 10.1007/s00020-014-2137-x

DO - 10.1007/s00020-014-2137-x

M3 - 期刊論文

AN - SCOPUS:84898905102

VL - 79

SP - 23

EP - 48

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 1

ER -