18 citations · 54 across the 16 of their papers we have counts for
15 papers · 1 filter
Weighted decoupling with lower-dimensional frequency localization
Jongchon Kim
We prove weighted and refined decoupling estimates for functions whose Fourier transforms are supported in a small neighborhood of the unit sphere or the truncated para…
A note on small cap square function and decoupling estimates for the parabola
Jongchon Kim, Liang Wang, Chun Keung Yeung
In this paper, we prove small cap square function and decoupling estimates for the parabola, where the small caps are essentially axis-parallel rectangles of dimensions $δ\times δ^…
Weighted wave envelope estimates for the parabola
Jongchon Kim, Hyerim Ko
In this paper, we extend the Córdoba-Fefferman square function estimate for the parabola to a weighted setting. Our weighted square function estimate is derived from a weighted wav…
Weighted decoupling estimates and the Bochner-Riesz means
Jongchon Kim
We prove new weighted decoupling estimates. As an application, we give an improved sufficient condition for almost everywhere convergence of the Bochner-Riesz means of arbitrary $L…
Nikodym sets and maximal functions associated with spheres
Alan Chang, Georgios Dosidis, Jongchon Kim
We study spherical analogues of Nikodym sets and related maximal functions. In particular, we prove sharp -estimates for Nikodym maximal functions associated with spheres. As…
Almost-orthogonality principles for certain directional maximal functions
Jongchon Kim
We develop almost-orthogonality principles for maximal functions associated with averages over line segments and directional singular integrals. Using them, we obtain sharp -b…
Bounds for a maximal directional Hilbert transform
Jongchon Kim, Malabika Pramanik
Given any finite direction set of cardinality in Euclidean space, we consider the maximal directional Hilbert transform associated to this direction set. Our main res…
Lower bounds for estimates of the Schrödinger maximal function
Xiumin Du, Jongchon Kim, Hong Wang +1
We give new lower bounds for estimates of the Schrödinger maximal function by generalizing an example of Bourgain.
Riesz means of Fourier series and integrals: Strong summability at the critical index
Jongchon Kim, Andreas Seeger
We consider spherical Riesz means of multiple Fourier series and some generalizations. While almost everywhere convergence of Riesz means at the critical index may fail f…
Some remarks on Fourier restriction estimates
Jongchon Kim
We provide refinements on some Fourier restriction estimates obtained using polynomial partitioning. Let be a compact surface with…
Endpoint bounds for a class of spectral multipliers on compact manifolds
Jongchon Kim
It is well known that the Stein-Tomas Fourier restriction theorem can be used to derive sharp bounds for radial Fourier multipliers such as the Bochner-Riesz means. In…
Endpoint bounds for quasiradial Fourier multipliers
Jongchon Kim
We consider quasiradial Fourier multipliers, i.e. multipliers of the form for a class of distance functions . We give a necessary and sufficient condition for the mult…
Endpoint bounds of square functions associated with Hankel multipliers
Jongchon Kim
We prove endpoint bounds for the square function associated with radial Fourier multipliers acting on radial functions. This is a consequence of endpoint bounds for a corre…
A characterization of maximal operators associated with radial Fourier multipliers
Jongchon Kim
We give a simple necessary and sufficient condition for maximal operators associated with radial Fourier multipliers to be bounded on and for certain greater…
On discrete fractional integral operators and related Diophantine equations
Jongchon Kim
We study discrete versions of fractional integral operators along curves and surfaces. estimates are obtained from upper bounds of the number of solutions of associat…