Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Multiparameter maximal functions along dilation-invariant hypersurfaces


Authors: Hasse Carlsson, Peter Sjögren and Jan-Olov Strömberg
Journal: Trans. Amer. Math. Soc. 292 (1985), 335-343
MSC: Primary 42B25
DOI: https://doi.org/10.1090/S0002-9947-1985-0805966-X
MathSciNet review: 805966
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Consider the hypersurface ${x_{n + 1}} = \Pi _1^nx_i^{{\alpha _i}}$ in ${{\mathbf {R}}^{n + 1}}$. The associated maximal function operator is defined as the supremum of means taken over those parts of the surface lying above the rectangles $\{ 0 \leqslant {x_i} \leqslant {h_i},\;i = 1, \ldots ,n\}$. We prove that this operator is bounded on ${L^p}$ for $p > 1$. An analogous result is proved for a quadratic surface in ${{\mathbf {R}}^3}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42B25

Retrieve articles in all journals with MSC: 42B25


Additional Information

Article copyright: © Copyright 1985 American Mathematical Society