Almost-orthogonality principles for certain directional maximal functions

Abstract

We develop almost-orthogonality principles for maximal functions associated with averages over line segments and directional singular integrals. Using them, we obtain sharp $L^2$-bounds for these maximal functions when the underlying direction set is equidistributed in ${\mathbb{S}}^{n-1}$.

A few typos are fixed, published (online) in The Journal of Geometric Analysis

References in corpus (5)

• Maximal directional operators along algebraic varieties
• A sharp estimate for the Hilbert transform along finite order lacunary sets of directions
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Cited by in corpus (1)

• Maximal subspace averages