є-Families of Operators in Triebel-Lizorkin and Tent Spaces

Welland, Grant ; Zhao, Shiying

Canadian journal of mathematics, Tome 47 (1995) no. 5, pp. 1095-1120

Résumé

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

Détail

DOI : 10.4153/CJM-1995-057-9

Mots-clés : 42B20, 42B25, Triebel-Lizorkin spaces, Besov spaces, tent spaces, є-families of operators, Calderón-Zygmund operators, vector-valued singular integrals, weights

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