$epsilon$-families of operators in Triebel-Lizorkin and tent spaces

Grant Welland, Shi Ying Zhao
1995 Canadian Journal of Mathematics - Journal Canadien de Mathematiques  
In this paper, we study the boundedness of e-families of operators on Triebel-Lizorkin with wide range of parameters. We also prove that e-families of operators are bounded from Triebel-Lizorkin spaces into (generalized) tent spaces, and obtain a characterization of certain Triebel-Lizorkin spaces in terms of tent spaces. In particular, the boundedness of fractional operators in Triebel-Lizorkin, and a sharp version of T\ theorem for generalized Calderôn-Zygmund operators on Triebel-Lizorkin
more » ... Triebel-Lizorkin spaces can be considered as applications of (proofs of) these results. of S t satisfies the following conditions: forx,y G W, and (1.2) \K t{x , y) -P^M^)\ < ij^]\ t+^l y lr^V for 2\y -z\ <t+ \x -y\, where (1.3) Pf_ z K t {^)= E ^T-DlK t (x 9 z) |7|<[£] 7 -
doi:10.4153/cjm-1995-057-9 fatcat:fqvvtipk6nemhi6zi4cgjuchn4