Joonil Kim

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-ÅyÅ¼wa, 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.CA2025

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 <…

math.CA2025

Restricted weak type endpoint estimate for the spherical maximal operators on the Heisenberg group

Hyunwoo Jeon, Joonil Kim

Let $H^{n}$ denote the Heisenberg group, identified with $R^{d} \times R$ , where $d = 2 n$ and $n \in N$ . We consider the spherical maximal operator…

math.CA2025

Lacunary elliptic maximal operator on the Heisenberg group

Joonil Kim, Jeongtae Oh

In this paper, we prove $ L^p $ boundedness results for lacunary elliptic maximal operators on the Heisenberg group. Furthermore, we extend these $ L^p $ estimates from skew-sy…