Abstract
The dimension-freeL 2-maximal inequality for convex symmetric bodies obtained in [2] is extended forp>3/2.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Bergh and J. Löfström,Interpolation Spaces, An Introduction, Springer, 1976.
J. Bourgain,On high dimensional maximal functions associated to convex bodies, preprint IHES; Amer. J. Math., to appear.
J. Bourgain,Estimation de certaines fonctions maximales, C. R. Acad. Sci. Paris, to appear.
E. M. Stein,Topics in Harmonic Analysis, Ann. Math. Studies No. 63, Princeton University Press, 1970.
E. M. Stein,Maximal functions, spherical means, Proc. Nat. Acad. Sci. USA73 (1976), 2174–2175.
E. M. Stein,Some results in harmonic analysis in R n,for n → ∞, Bull. Amer. Math. Soc.9 (1983), 71–73.
E. M. Stein and J. O. Stromberg,Behavior of maximal functions in R n for large n, Ark. Mat.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bourgain, J. On theL p-bounds for maximal functions associated to convex bodies inR n . Israel J. Math. 54, 257–265 (1986). https://doi.org/10.1007/BF02764955
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02764955