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Lp Decay Estimates for Circular Means of Fractal Measures in ℝ2
Abstract
In this paper, we investigate weighted Lp→ Lq restriction estimates for the Fourier extension operator associated with planar curves of non-vanishing curvature. More precisely, we establish estimates of the form |Ef|Lq(X)≤ CεRε|f|p, where X is an α-dimensional set. As an application of this result, we derive a new Lp decay estimate for circular means of Fourier transforms of fractal measures in ℝ2. We also construct examples that give several upper bounds for the decay exponent when p∈[1,2].
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BibTeX
@misc{cao2026decay,
title = {{$L^p$ Decay Estimates for Circular Means of Fractal Measures in $\mathbbR^2$}},
author = {Zhenbin Cao and Feilong Guo and Junfeng Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.20108},
eprint = {2609.20108},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20108},
}
RIS
TY - UNPB
TI - L^p Decay Estimates for Circular Means of Fractal Measures in ℝ^2
AU - Zhenbin Cao
AU - Feilong Guo
AU - Junfeng Li
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2609.20108
UR - https://arxiv.org/abs/2609.20108
AB - In this paper, we investigate weighted L^p→ L^q restriction estimates for the Fourier extension operator associated with planar curves of non-vanishing curvature. More precisely, we establish estimates of the form |Ef|_L^q(X)≤ C_εR^ε|f|_p, where X is an α-dimensional set. As an application of this result, we derive a new L^p decay estimate for circular means of Fourier transforms of fractal measures in ℝ^2. We also construct examples that give several upper bounds for the decay exponent when p∈[1,2].
ER -