Abstract
AbstractFor $$p \in [2,\infty )$$
p
∈
[
2
,
∞
)
, we consider the $$L^p \rightarrow L^p$$
L
p
→
L
p
boundedness of a Nikodym maximal function associated to a one-parameter family of tubes in $${\mathbb {R}}^{d+1}$$
R
d
+
1
whose directions are determined by a non-degenerate curve $$\gamma $$
γ
in $${\mathbb {R}}^d$$
R
d
. These operators arise in the analysis of maximal averages over space curves. The main theorem generalises the known results for $$d = 2$$
d
=
2
and $$d = 3$$
d
=
3
to general dimensions. The key ingredient is an induction scheme motivated by recent work of Ko-Lee-Oh.
Publisher
Springer Science and Business Media LLC
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