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arXiv · 1210.7379

Maximal Functions for Lacunary Dilation Structures

Patrick LaVictoire
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Abstract

If mu is a smooth density on a hypersurface in R^d whose curvature never vanishes to infinite order, and A is a d-by-d matrix whose eigenvalues all have absolute value greater than 1, then the maximal function given by convolving f with dilates of mu by powers of A, and taking the maximum, is bounded from a corresponding version of H^1 to weak L^1.

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Patrick LaVictoire. 2012-10-27. Maximal Functions for Lacunary Dilation Structures. https://arxiv.org/abs/1210.7379

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