10 papers
Orthonormal Strichartz estimates over fractal time
Guoxia Feng, Jinbong Lee, Sanghyuk Lee
We study Strichartz estimates for orthonormal families of initial data when time is integrated against an -dimensional Frostman measure , , with coefficients measure…
On the endpoint estimate for discrete spherical average over sparse sequences
Sanghyuk Lee, Ji Li, Chong-Wei Liang +2
Let , and let denote the normalized discrete spherical average on with squared radius . For a strictly increasing sequence of positive intege…
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…
The Endpoint Eigenfunction Bound for the Hermite Operator in Two Dimensions
Eunhee Jeong, Sanghyuk Lee, Jaehyeon Ryu
In this paper, we establish the optimal \(L^2(\mathbb{R}^2)\to L^{10/3}(\mathbb{R}^2)\) endpoint estimate for the spectral projection operator associated with the Hermite operator…
Sharpness of convolution bounds for measures
Sanghyuk Lee, Sungchul Lee
In this paper, we determine the optimal universal \(L^p\)-\(L^q\) type sets for convolution operators \(f\mapsto μ*f\) associated with fractal measures $μ\in \mathcal P_{α,β}(\math…
Strichartz and local smoothing estimates for the fractional Schrödinger equations over fractal time
Jin Bong Lee, Sanghyuk Lee, Luz Roncal
We obtain Strichartz-type estimates for the fractional Schrödinger operator over a time set of fractal dimension. To obtain those estimates captu…
Endpoint estimates for the fractal circular maximal function and related local smoothing
Sanghyuk Lee, Luz Roncal, Feng Zhang +1
Sharp -- estimates for the spherical maximal function over dilation sets of fractal dimensions, including the endpoint estimates, were recently proved by Anderson--Hughes…
Damping oscillatory Integrals of convex analytic functions
Sanghyuk Lee, Sewook Oh
Let be a compact, convex, analytic hypersurface of finite type with a smooth measure on . Let denote the Gaussian curvature on . We consider the o…
Endpoint estimates for maximal operators associated to the wave equation
Chu-Hee Cho, Sanghyuk Lee, Wenjuan Li
We consider the -- maximal estimates associated to the wave operator \begin{equation*} e^{ it\sqrt{-Δ}}f(x) = \frac{1}{(2π)^d}\int_{\mathbb{R}^d} e^{i(x \cdot ξ\, + t|ξ…
Bochner-Riesz mean for the twisted Laplacian in
Eunhee Jeong, Sanghyuk Lee, Jaehyeon Ryu
We study the Bochner-Riesz problem for the twisted Laplacian on . For , it has been conjectured that the Bochner-Riesz mea…