Ultraspherical multipliers revisited

Turán's inequality for ultraspherical polynomials revisited

We present a short proof that the normalized Turán determinant in the ultraspherical case is convex or concave depending on whether parameter $λ$ is positive or negative.

加权谱簇界与超球Grushin算子的尖锐乘子定理

Weighted spectral cluster bounds and a sharp multiplier theorem for ultraspherical Grushin operators

本文研究d维球面上在k维球面处奇异的Grushin型退化椭圆算子，通过建立加权谱簇界和超球多项式精确估计，证明了在2k≤d时最优的Mihlin-Hörmander型谱乘子定理及Bochner-Riesz可求和性结果。

The Marcinkiewicz multiplier theorem revisited

We provide a complete proof of an optimal version of the Marcinkiewicz multiplier theorem.

Singular integrals and maximal functions: the disk multiplier revisited

Several estimates for singular integrals, maximal functions and the spherical summation operator are given in the spaces $L^p_{\text{rad}}L^2_{\text{ang}}(\mathbb{R}^n)$, $n\geq 2$.

Fourier Multipliers on the Heisenberg groups revisited

In this paper, we give explicit expressions of differential-difference operators appeared in the hypothesis of the general Fourier multiplier theorem associated to the Heisenberg groups proved by Mauceri and De Micheal for one dimension and C. Lin for higher dimension. We also give a much shorter proof of the above-mentioned theorem. Then we obtain a sharp weighted estimate for Fourier multipliers on the Heisenberg groups.