Abstract
For all d >= 2 and P epsilon (1, max(2, (d + 1)/2)], we prove sharp L-p to L-p(L-q) estimates (modulo an endpoint) for a directional maximal operator associated to curves generated by the dilation matrices exp((log t)P), where P has real entries and eigenvalues with positive real part. For the corresponding Hilbert transform we prove an analogous result for all d >= 2 and P epsilon (1, 2]. As corollaries, we prove L-p bounds for variable kernel singular integral operators and Nikodym-type maximal operators taking averages over certain families of curved sets in R-d. (C) 2008 Elsevier Inc. All rights reserved.
Original language | English |
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Pages (from-to) | 3281-3302 |
Number of pages | 22 |
Journal | Journal of Functional Analysis |
Volume | 255 |
Issue number | 12 |
DOIs | |
Publication status | Published - 15 Dec 2008 |
Keywords
- Nonisotropic
- Mixed-norm estimates
- Hilbert transform
- Maximal operator