Yaryong Heo
Korea University · Mathematics
About the Lab
Professor Yaryong Heo's research lab specializes in harmonic analysis, with a focus on Fourier multipliers, restriction estimates, and regularity properties of operators associated with singular and non-smooth surfaces in high-dimensional spaces. The lab investigates radial and conical multipliers, maximal operators over non-convex and non-smooth hypersurfaces, and sharp $L^p$ estimates for averaging and wave-type operators. Their work often combines advanced techniques such as refined Calderón-Zygmund decompositions and restriction theory to derive endpoint bounds and new regularity results in high dimensions.
Research Overview
Research Output Trend
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Selected Papers
15Given a fixed p≠2, we prove a simple and effective characterization of all radial multipliers of $ \mathcal{F}{L^p}\left( {{\mathbb{R}^d}} \right) $, provided that the dimension d is sufficiently large. The method also yields new Lq space-time regularity results for solutions of the wave equation in high dimensions.
We obtain some improved bounds for high dimensional cone multipliers by combining the well-known L 2 cone restriction estimate with a refined Calderon-Zygmund decomposition which comes under the consideration of the support of the kernel.
In this paper we consider an endpoint estimate for high-dimensional cone multipliers.
In this paper we establish sharp <TEX>$L^p$</TEX>-regularity estimates for averaging operators with convolution kernel associated to hypersurfaces in <TEX>$\mathbb{R}^d(d{\geq}2)$</TEX> of the form <TEX>$y{\mapsto}(y,{\gamma}(y))$</TEX> where <TEX>$y{\in}\mathbb{R}^{d-1}$</TEX> and <TEX>${\gamma}(y)={\sum}^{d-1}_{i=1}{\pm}{\mid}y_i{\mid}^{m_i}$</TEX> with <TEX>$2{\leq}m_1{\leq}{\cdots}{\leq}m_</TEX><TEX>{d-1}$</TEX>.
Research Areas
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