New Besov-type spaces and Triebel-Lizorkin-type spaces including Q spaces

作者：Yang, Dachun^*; Yuan, Wen

来源：Mathematische Zeitschrift, 2010, 265(2): 451-480.

DOI：10.1007/s00209-009-0524-9

• Besov space
• Triebel-Lizorkin space
• Q space
• Tent space
• Hardy-Hausdorff space
• Dual space
• Hausdorff capacity
• Calderon reproducing formula
• phi-transform
• Embedding
• Lifting
• Almost diagonal operator
• Atom
• Molecule

Let s, tau is an element of R and q is an element of (0, infinity]. We introduce Besov-type spaces. (B) over dot(p, q)(s, tau) (R-n) for p is an element of (0, infinity] and Triebel-Lizorkin-type spaces. (F) over dot(p, q)(s, tau)(R-n) for p is an element of (0, infinity), which unify and generalize the Besov spaces, Triebel-Lizorkin spaces and Q spaces. We then establish the phi-transform characterization of these new spaces in the sense of Frazier and Jawerth. Using the phi-transform characterization of (B) over dot(p, q)(s, tau) (R-n) and (F) over dot(p, q)(s, tau)(R-n), we obtain their embedding and lifting properties; moreover, for appropriate tau, we also establish the smooth atomic and molecular decomposition characterizations of (B) over dot(p, q)(s, tau)(R-n) and (F) over dot(p, q)(s, tau)(R-n). For s is an element of R, p is an element of (1, infinity), q is an element of [1, infinity) and tau is an element of [0, 1/(max{p, q})'], via the Hausdorff capacity, we introduce certain Hardy-Hausdorff spaces B(H) over dot(p, q)(s, tau)(R-n) and prove that the dual space of B(H) over dot(p, q)(s, tau)(R-n) is just (B) over dot(p', q')(s, tau)(R-n), where t' denotes the conjugate index of t is an element of (1, infinity).

• 出版日期2010-6
• 单位北京师范大学