7 papers
On the endpoint estimate for discrete spherical average over sparse sequences
Sanghyuk Lee, Ji Li, Chong-wei Liang +1
Let . For a lacunary sequence of radii in the \emph{highly composite} regime, that is with as ,…
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}(\…
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 ca…
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{-Î}}f(x) = \frac{1}{(2Ï)^d}\int_{\mathbb{R}^d} e^{i(x \cdot ξ\, +…
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…