A NEW CHARACTERIZATION OF TRIEBEL-LIZORKIN SPACES ON Rn

作者：Yang, Dachun^*; Yuan, Wen; Zhou, Yuan

来源：Publicacions Matematiques, 2013, 57(1): 57-82.

DOI：10.5565/PUBLMAT_57113_02

• Triebel-Lizorkin space
• Besov space
• square function
• Calderon reproducing formula

In this paper, the authors characterize the Triebel-Lizorkin space (F) over dot(p,q)(alpha)(R-n) via a new square function @@@ S-alpha,S-q(f)(x) = {Sigma(k is an element of Z)2(k alpha q)vertical bar 1/vertical bar B(x, 2(-k))vertical bar integral(B(x, 2-k))[f(x) - f(y)]dy vertical bar(q)|(1/q), @@@ where f is an element of L-loc(1)(R-n) boolean AND S'(R-n), x is an element of R-n, alpha is an element of (0,2) and p, q is an element of (1,infinity]. Similar characterizations are also established for Triebel-Lizorkin spaces (F) over dot(p,q)(alpha)(R-n) with alpha is an element of (0, infinity)\2N and p,q is an element of (1, infinity], and for Besov spaces (B) over dot(p,q)(alpha)(R-n) with alpha is an element of (0, infinity) \ 2N, p not subset of (1, infinity] and q is an element of (0, infinity].

• 出版日期2013
• 单位北京师范大学; 北京航空航天大学