Sanghyuk Lee

activity

20192023

collaborators

5 papers

math.CA2023

$L^{p}$ bound on the strong spherical maximal function

Juyoung Lee, Sanghyuk Lee, Sewook Oh

In this note we show that the strong spherical maximal function in $R^{d}$ is bounded on $L^{p}$ if $p > 2 (d + 1) / (d - 1)$ for $d \geq 3$ .

math.CA2023

The elliptic maximal function

Juyoung Lee, Sanghyuk Lee, Sewook Oh

We study the elliptic maximal functions defined by averages over ellipses and rotated ellipses which are multi-parametric variants of the circular maximal function. We prove that t…

math.CA2022

$L^{p}$ maximal bound and Sobolev regularity of two-parameter averages over tori

Juyoung Lee, Sanghyuk Lee

We investigate $L^{p}$ boundedness of the maximal function defined by the averaging operator $f \to A_{t}^{s} f$ over the two-parameter family of tori $\mathbb{T}_t^{s}:=\{ ( (t…

math.CA2021

$L^{p} - L^{q}$ estimates for the circular maximal operators on Heisenberg radial functions

Juyoung Lee, Sanghyuk Lee

$L^{p}$ boundedness of the circular maximal function $M_{H^{1}}$ on the Heisenberg group $H^{1}$ has received considerable attentions. While the problem still…

math.CA2019

Restriction estimates to complex hypersurfaces

Juyoung Lee, Sanghyuk Lee

The restriction problem is better understood for hypersurfaces and recent progresses have been made by bilinear and multilinear approaches and most recently polynomial partitioning…

Lp bound on the strong spherical maximal function

The elliptic maximal function

Lp maximal bound and Sobolev regularity of two-parameter averages over tori

Lp−Lq estimates for the circular maximal operators on Heisenberg radial functions

Restriction estimates to complex hypersurfaces

$L^{p}$ bound on the strong spherical maximal function

$L^{p}$ maximal bound and Sobolev regularity of two-parameter averages over tori

$L^{p} - L^{q}$ estimates for the circular maximal operators on Heisenberg radial functions