Dual Properties of Triebel–Lizorkin-Type Spaces and their Applications

  • Dachun Yang

    Beijing Normal University, China
  • Wen Yuan

    Beijing Normal University, China


Let , , and be the set of all Schwartz functions whose Fourier transforms satisfy that for all . Denote by the closure of in the Triebel–Lizorkin-type space . In this paper, the authors prove that the dual space of is the Triebel–Lizorkin–Hausdorff space via their -transform characterizations together with the atomic decomposition characterization of the tent space , where denotes the conjugate index of . This gives a generalization of the well-known duality that by taking , and . As applications, the authors obtain the Sobolev-type embedding property, the smooth atomic and molecular decomposition characterizations, boundednesses of both pseudo-differential operators and the trace operators on ; all of these results improve the existing conclusions.

Cite this article

Dachun Yang, Wen Yuan, Dual Properties of Triebel–Lizorkin-Type Spaces and their Applications. Z. Anal. Anwend. 30 (2011), no. 1, pp. 29–58

DOI 10.4171/ZAA/1422