A note on the spherical maximal operator for radial functions
HTML articles powered by AMS MathViewer
- by Mark Leckband PDF
- Proc. Amer. Math. Soc. 100 (1987), 635-640 Request permission
Abstract:
The spherical maximal operator for radial functions of ${{\mathbf {R}}^n}$ is shown to be a restricted weak type ${L^p}$ bounded operator for $p = n/(n - 1)$. The proof uses methods for restricted weak type single weight norm inequalities.References
- J. Bourgain, Averages in the plane over convex curves and maximal operators, J. Analyse Math. 47 (1986), 69–85. MR 874045, DOI 10.1007/BF02792533
- M. A. Leckband and C. J. Neugebauer, A general maximal operator and the $A_{p}$-condition, Trans. Amer. Math. Soc. 275 (1983), no. 2, 821–831. MR 682735, DOI 10.1090/S0002-9947-1983-0682735-3
- Benjamin Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207–226. MR 293384, DOI 10.1090/S0002-9947-1972-0293384-6
- Elias M. Stein and Stephen Wainger, Problems in harmonic analysis related to curvature, Bull. Amer. Math. Soc. 84 (1978), no. 6, 1239–1295. MR 508453, DOI 10.1090/S0002-9904-1978-14554-6
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 635-640
- MSC: Primary 42B25
- DOI: https://doi.org/10.1090/S0002-9939-1987-0894429-9
- MathSciNet review: 894429