Abstract
The Carleson operator is closely related to the maximal partial sum operator for Fourier series. We study generalizations of this operator in one and several variables.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Carleson, L. (1966). On convergence and growth of partial sums of Fourier series,Acta Math. 111, 135–157.
Fefferman, C. (1973). Pointwise convergence of Fourier series,Ann. Math.,98, 551–571.
García-Cuerva, J. and Rubio de Francia, J.L. (1985).Weighted Norm Inequalities and Related Topics, Mathematics studies, North-Holland.
Hunt, R.A. (1968).On the convergence of Fourier series, Orthogonal expansions and their continuous analogues, Proceedings of the Conference held at Southern Illinois University, Edwardsville, 1967. SIU Press, Carbondale, IL.
Prestini, E. Singular integrals on product spaces related to Carleson operator, preprint.
Rubio de Francia, J.L., Ruiz, F.J., and Torrea, J.L. (1986). Calderón-Zygmund theory for operator-valued kernels,Adv. Math.,62, 7–48.
Sjölin, P. (1971). Convergence almost everywhere of certain singular integrals and multiple Fourier series,Arkiv f. matematik,9, 65–90.
Stein, E.M. (1970).Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ.
Author information
Authors and Affiliations
Additional information
Communicated by T. Körner
Rights and permissions
About this article
Cite this article
Prestini, E., Sjölin, P. A littlewood-paley inequality for the Carleson operator. The Journal of Fourier Analysis and Applications 6, 457–466 (2000). https://doi.org/10.1007/BF02511540
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02511540