Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-06-25T20:33:12.428Z Has data issue: false hasContentIssue false
  • English
  • Français

Remarks on square functions in the Littlewood-Paley theory

Published online by Cambridge University Press:  17 April 2009

Shuichi Sato
Shuichi Sato
Affiliation:
Department of Mathematics, Faculty of Education, Kanazawa University, Kanazawa 920–11, Japan e-mail: shuichi@kenroku.ipc.kanazawa-u.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove that certain square function operators in the Littlewood-Paley theory defined by the kernels without any regularity are bounded on , 1 < p < ∞, w ∈ Ap (the weights of Muckenhoupt). Then, we give some applications to the Carleson measures on the upper half space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 58 , Issue 2 , October 1998 , pp. 199 - 211
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Benedek, A., Calderón, A.P. and Panzone, R., ‘Convolution operators on Banach space valued functions’, Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 356–365.CrossRefGoogle ScholarPubMed
[2]Christ, M., Lectures on singular integral operators, Regional conference series in mathematics 77 (Amer. Math. Soc., Providence, R.I., 1990).Google Scholar
[3]Coifman, R.R. and Meyer, Y., Au delà des opérateurs pseudo-différentiels, Astérisque 57 (Soc. Math. France, 1978).Google Scholar
[4]Duoandikoetxea, J., ‘Weighted norm inequalities for homogeneous singular integrals’, Trans. Amer. Math. Soc. 336 (1993), 869–880.CrossRefGoogle Scholar
[5]Duoandikoetxea, J. and de Francia, J.L. Rubio, ‘Maximal and singular integral operators via Fourier transform estimates’, Invent. Math. 84 (1986), 541–561.CrossRefGoogle Scholar
[6]Garcia-Cuerva, J. and de Francia, J.L. Rubio, Weighted norm inequalities and related topics (North-Holland Publishing Co, Amsterdam, 1985).Google Scholar
[7]Journé, J.-L.Calderón-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderón, Lecture Notes in Math. 994 (Springer-Verlag, 1983).CrossRefGoogle Scholar
[8]de Francia, J.L. Rubio, ‘Factorization theory and Ap weights’, Amer. J. Math. 106 (1984), 533–547.CrossRefGoogle Scholar
[9]Stein, E. M., ‘On the functions of Littlewood-Paley, Lusin, and Marcinkiewicz’, Trans. Amer. Math. Soc. 88 (1958), 430–466.CrossRefGoogle Scholar
[10]Stein, E. M., Singular integrals and differentiability properties of functions (Princeton Univ. Press, Princeton, N.J., 1970).Google Scholar