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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

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 5 , 01 October 1995 , pp. 1095 - 1120
Copyright
Copyright © Canadian Mathematical Society 1995

References

[AJ] Andersen, K.F. and John, R.T., Weighted inequalities for vector-valued maximalfunctions and singular integrals, Studia Math. 69(1980), 19–31.Google Scholar
[CT] Calderón, A. P. and Torchinsky, A., Parabolic maximal functions associated with a distribution, Adv. Math. 16(1979), 1–64.Google Scholar
[C J] Christ, M. and Journé, J.-L., Polynomial growth estimates for multilinear singular integral operators, Acta Math. 159(1987), 51–80.Google Scholar
[CDMS] Coifman, R., David, G., Meyer, Y. and Semmes, S., ω-Calderón-Zygmund operators, Proceedings of the Conference on Harmonic Analysis and Partial Differential Equations, Lecture Notes in Math. 1384, (ed. Garcia-Cuerva, J.), Springer-Verlag, Berlin and Heidelberg, 1989. 132–145.Google Scholar
[CMS] Coifman, R., Meyer, Y. and Stein, E.M., Some new function spaces and their applications to harmonic analysis, J. Funct. Anal. 62(1985), 304–335.Google Scholar
[GR] García-Cuerva, J. and de Francia, J.L.Rubio, Weighted Norm Inequalities and Related Topics, North- Holland Math. Studies 116 North-Holland, Amsterdam, 1985.Google Scholar
[HI] Han, Y.-S., Calderón-type reproducing formula and the Tb theorem, Rev. Mat. Iberoamericana 10(1994), 51–91.Google Scholar
[H2] Han, Y.-S., Triebel-Lizorkin spaces on spaces of homogeneous type, Studia Math. 108(1994), 247–273.Google Scholar
[HH] Han, Y.-S. and Hofmann!, S. 77 theorems for Besov and Triebel-Lizorkin spaces, Trans. Amer. Math. Soc. 337(1993), 839–853.Google Scholar
[HJTW] Han, Y.-S., Jawerth, B., Taibleson, M. and Weiss, G., Littlewood-Paley theory and e-families of operators,, Collect. Math. 50/ 51(1990), 1–39.Google Scholar
[HS] Han, Y.-S. and Sawyer, E.T., Para-accretive functions, the weak boundedness property and the Tb theorem,, Rev. Mat. Iberoamericana 6(1990), 17–41.Google Scholar
[P] Peetre, J., On spaces of Triebel-Lizorkin type, Ark. Mat. 13(1975), 123–130.Google Scholar
[RRT] de Francia, J.L.Rubio, Ruiz, F.J. and Torrea, J.L., Calderôn-Zygmund theory for operator-valued kernels, Adv. Math. 62(1986), 7–48.Google Scholar
[S] Stein, E.M., Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, New Jersey, 1970.Google Scholar
[ST] Strömberg, J.-O. and Torchinsky, A., Weighted Hardy Spaces, Lecture Notes in Math. 1381, Springer- Verlag, Berlin and Heidelberg, 1989.Google Scholar
[Tor] Torchinsky, A., Real-Variable Methods in Harmonic Analysis, Academic Press, Orlando, 1986.Google Scholar
[T] Torres, R.H., Boundedness results for operators with singular kernels on distribution spaces, Mem. Amer. Math. Soc. 442(1991).Google Scholar
[Tr] Triebel, H., Theory of Function Spaces, Birkhàuser Basel, 1983.Google Scholar