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Transactions of the American Mathematical Society

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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
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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}$.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0805966-X
Article copyright: © Copyright 1985 American Mathematical Society

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