허야용 교수

Given 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>.