Juyoung Lee

activity

20172026

collaborators

11 papers

math.CA2026

Endpoint power weight inequalities for spherical maximal functions

Marco Fraccaroli, Juyoung Lee, Nikou Lei +2

We prove sharp $L^{p} (∣ x ∣^{α})$ estimate for spherical maximal functions. We resolve the remaining open problem for the full maximal operator for $α = 1 - d$ and $p < 2$ and prove a more gen…

math.CA2026

Two-parameter variational estimates for averages over tori

Juyoung Lee, Sanghyuk Lee, Feng Zhang +1

One-parameter variational inequalities are well developed, whereas their multi-parameter counterparts remain much less understood. We explore two-parameter variational inequalities…

math.CA2026

Directional maximal operators in the plane

Edward Kroc, Juyoung Lee, Malabika Pramanik

This monograph investigates the Lebesgue boundedness of planar directional maximal operators $D_{Ω}$ . These are maximal averages of functions over line segments in $R^{2}$ whos…

math.CA2026

Maximal averages and non-transversality

Jin Bong Lee, Juyoung Lee, Jeongtae Oh +1

We investigate the $L^{p}$ mapping properties of maximal functions associated with analytic hypersurfaces in $R^{d}$ , with a particular emphasis on the role of transversality.…

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 critical weighted inequalities of the spherical maximal function

Juyoung Lee

Weighted inequality on the Hardy-Littlewood maximal function is completely understood while it is not well understood for the spherical maximal function. For the power weight $|x|^…

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…

math.GR2017

Finite subgraphs of an extension graph

Sang-hyun Kim, Thomas Koberda, Juyoung Lee

Let $Γ$ be a finite graph and let $Γ^{e}$ be its extension graph. We inductively define a sequence ${Γ_{i}}$ of finite induced subgraphs of $Γ^{e}$ through succes…

Endpoint power weight inequalities for spherical maximal functions

Two-parameter variational estimates for averages over tori

Directional maximal operators in the plane

Maximal averages and non-transversality

Lp bound on the strong spherical maximal function

The critical weighted inequalities of the 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

Finite subgraphs of an extension graph

$L^{p}$ 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