EPSILON-FAMILIES OF OPERATORS IN TRIEBEL-LIZORKIN AND TENT SPACES

In this paper, we study the boundedness of E-families of operators on Triebel-Lizorkin with wide range of parameters. We also prove that epsilon-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 Tl theorem for generalized Calderon-Zygmund operators on Triebel-Lizorkin spaces can be considered as applications of (proofs of) these results.