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

Published online by Cambridge University Press:  20 November 2018

Grant Welland  and
Shiying Zhao
Grant Welland
Affiliation:
Department of Mathematics and Computer Science, University of Missouri-St. Louis, St. Louis, Missouri 63121, U.S.A.
Shiying Zhao
Affiliation:
Department of Mathematics and Computer Science, University of Missouri-St. Louis, St. Louis, Missouri 63121, U.S.A.
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Abstract

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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.

Keywords

42B2042B25Triebel-Lizorkin spacesBesov spacestent spacesє-families of operatorsCalderón-Zygmund operatorsvector-valued singular integralsweights
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 5 , 01 October 1995 , pp. 1095 - 1120
Copyright
Copyright © Canadian Mathematical Society 1995

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