arXiv subjects

Chu-hee Cho

Publications and source records attributed to Chu-hee Cho.

7 recordsLinked to original sources

arXiv2026

Sharp $L^2$ Estimates for $(2+1)$-dimensional oscillatory integral operators with homogeneous binomial phases

We study oscillatory integral operators in $(2+1)$-dimensions with a homogeneous binomial phase \[ \Phi(x,y,t)=x^{k-k_P}t^{k_P}+y^{k-k_Q}t^{k_Q}, \qquad 1\le k_P<k_Q<k. \] For compactly supported smooth amplitudes, we establish sharp $L^2(\R)\to L^2(\R^2)$ estimates with logarithmic losses occurring only in certain critical cases. The proof is based on scale-dependent Phong--Stein estimates.

math.CA↗

arXiv2023

$L^p$ improving properties and maximal estimates for certain multilinear averaging operators

In this article we focus on $L^{p}$ estimates for two types of multilinear lacunary maximal averages over hypersurfaces with curvature conditions. Moreover, we give a different proof for the bilinear lacunary spherical maximal functions. To obtain our results, we make use of the $L^1$-improving estimates of multilinear averaging operators. We also obtain $L^p$-improving estimates for certain multilinear averages by means of the nonlinear Brascamp-Lieb inequality.

math.CA↗

arXiv2022

Dimension of divergence sets of oscillatory integrals with concave phase

We study the Hausdorff dimension of the sets on which the pointwise convergence of the solutions to the fractional Schr\"odinger equation $e^{it(-\Delta)^\frac m2}f$ fails when $m\in(0,1)$ in one spatial dimension. The pointwise convergence along a non-tangential curve and a set of lines are also considered, where we find different nature from the case when $m\in(1,\infty)$.

math.AP↗

arXiv2022

A note on some variations of the maximal inequality for the fractional Schr\"odinger equation

The purpose of this note is to provide a summary of the recent work of the authors on two variations of the pointwise convergence problem for the solutions to the fractional Schr\"odinger equations; convergence along a tangential line and along a set of lines, as exhibiting some new results in each setting. For the former case, we make a simple observation on a path along a tangential curve of exponential order. We discuss counterexamples for the latter case that show some of the known smooth regularities are essentially optimal.

math.AP↗

arXiv2021

Pointwise convergence of the fractional Schrödinger equation in $\mathbb R^2$

We investigate the pointwise convergence of the solution to the fractional Schrödinger equation in $\mathbb R^2$. By establishing $H^s(\mathbb R^2)-L^3(\mathbb R^2)$ estimates for the associated maximal operator provided that $s>1/3$, we improve the previous result obtained by Miao, Yang, and Zheng. Our estimates extend the refined Strichartz estimates obtained by Du, Guth, and Li to a general class of elliptic functions.

math.AP↗

arXiv2021

A global space-time estimate for dispersive operators through its local estimate

We will show that a local space-time estimate implies a global space-time estimate for dispersive operators. In order for this implication we consider a Littlewood-Paley type square function estimate for dispersive operators in a time variable and a generalization of Tao's epsilon removal lemma in mixed norms. By applying this implication to the fractional Schrodinger equation in R^{2+1} we obtain the sharp global space-time estimates with optimal regularity from the previous known local ones.

math.AP↗

arXiv2020

Pointwise convergence along a tangential curve for the fractional Schrödinger equation

In this paper we study the pointwise convergence problem along a tangential curve for the fractional Schrödinger equations in one spatial dimension and estimate the capacitary dimension of the divergence set. We extend a prior paper by Lee and the first author for the classical Schrödinger equation, which in itself contains a result due to Lee, Vargas and the first author, to the fractional Schrödinger equation. The proof is based on a decomposition argument without time localization, which has recently been introduced by the second author.

math.AP↗