Hoyoung Song

activity

20222026

collaborators

5 papers

math.CA2026

Multi-Parameter Exponential Sums with Product Hilbert Kernels

Joonil Kim, Hoyoung Song

We establish necessary and sufficient conditions for the uniform boundedness of the multi-parameter exponential sums with product Hilbert kernels $$\sum_{1\le|t_1|\le N_1,\cdots,1\…

math.CA2026

Discrete analogues in harmonic analysis: Multi-parameter Radon averages

Agnieszka Hejna-Łyżwa, Joonil Kim, Bartosz Langowski +3

In this paper we study maximal and oscillation inequalities for multi-parameter discrete Radon averaging operators. We develop a robust variant of the multi-parameter circle method…

math.CA2023

Weak type 1-1 bound of multi-parameter maximal function

Hoyoung Song

We define the mulati-parameter maximal function $M$ as $$ \mathcal{M} f(x)=\sup _{0<h_1,h_2,\cdots,h_n<1} \frac{1}{h_1h_2\cdots h_n}\left|\int_0^{h_1}\cdots \int_0^{h_n}…

math.CA2023

The Proof of restriction conjecture In $R^{3}$

Hoyoung Song

If S is a smooth compact surface in $R^{3}$ with strictly positive second fundamental form, and $E_{S}$ is the corresponding extension operator, then we prove that for all $…

math.CA2022

Discrete Double Hilbert Transforms Along Polynomial Surfaces

Joonil Kim, Hoyoung Song

We obtain a necessary and sufficient condition on a polynomial $P (t_{1}, t_{2})$ for the $ℓ^{p}$ boundedness of the discrete double Hilbert transforms associated with $P (t)$ for $1 <…

Multi-Parameter Exponential Sums with Product Hilbert Kernels

Discrete analogues in harmonic analysis: Multi-parameter Radon averages

Weak type 1-1 bound of multi-parameter maximal function

The Proof of restriction conjecture In R3

Discrete Double Hilbert Transforms Along Polynomial Surfaces

The Proof of restriction conjecture In $R^{3}$