arXiv subjects

Aswin Govindan Sheri

Publications and source records attributed to Aswin Govindan Sheri.

2 recordsLinked to original sources

arXiv2023

Lacunary maximal functions on homogeneous groups

We observe that classical arguments of Ricci--Stein can be used to prove $L^p$ bounds for maximal functions associated to lacunary dilates of a fixed measure in the setting of homogenous groups. This recovers some recent results on averages over Korányi spheres and horizontal spherical averages of a type introduced by Nevo--Thangavelu. Moreover, the main theorem applies much more broadly and we explore its consequences through a variety of explicit examples.

math.CA↗

arXiv2022

$L^2$ estimates for a Nikodym maximal function associated to space curves

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

math.CA↗