Hankel Multipliers And Transplantation Operators

Hankel 变换移植算子的一致加权不等式

Uniform weighted inequalities for the Hankel transform transplantation operator

该研究建立 Hankel 变换移植算子的一致加权及加权向量值不等式，并据此推广 Rubio de Francia 的迁移定理。

On weighted transplantation and multipliers for Laguerre expansions

Using the standard square--function method (based on the Poisson semigroup), multiplier conditions of Hörmander type are derived for Laguerre expansions in $L^p$--spaces with power weights in the $A_p$-range; this result can be interpreted as an ``upper end point'' multiplier criterion which is fairly good for $p$ near $1$ or near $\infty $. A weighted generalization of Kanjin's \cite{kan} transplantation theorem allows to obtain a ``lower end point'' multiplier criterion whence by interpolation nearly ``optimal'' multiplier criteria (in dependance of $p$, the order of the Laguerre polynomial,…

Endpoint bounds of square functions associated with Hankel multipliers

We prove endpoint bounds for the square function associated with radial Fourier multipliers acting on $L^{p}$ radial functions. This is a consequence of endpoint bounds for a corresponding square function for Hankel multipliers. We obtain a sharp Marcinkiewicz-type multiplier theorem for multivariate Hankel multipliers and $L^p$ bounds of maximal operators generated by Hankel multipliers as corollaries. The proof is built on techniques developed by Garrigós and Seeger for characterizations of Hankel multipliers.

Characterizations of Hankel multipliers

We give characterizations of radial Fourier multipliers as acting on radial L^p-functions, 1<p<2d/(d+1), in terms of Lebesgue space norms for Fourier localized pieces of the convolution kernel. This is a special case of corresponding results for general Hankel multipliers. Besides L^p-L^q bounds we also characterize weak type inequalities and intermediate inequalities involving Lorentz spaces. Applications include results on interpolation of multiplier spaces.

Hankel and Toeplitz-Schur Multipliers

We study the problem of characterizing Hankel-Schur multipliers and Toeplitz-Schur multipliers of Schatten-von Neumann class $\bS_p$ for $0<p<1$. We obtain various sharp necessary conditions and sufficient conditions for a Hankel matrix to be a Schur multiplier of $\bS_p$. We also give a characterization of the Hankel-Schur multipliers of $\bS_p$ whose symbols have lacunary power series. Then the results on Hankel-Schur multipliers are used to obtain a characterization of the Toeplitz-Schur multipliers of $\bS_p$. Finally, we return to Hankel-Schur multipliers and obtain new results in the cas…

多圆盘中的对数 Bloch 空间、Hankel 算子的端点结果与逐点乘子

Logarithmic Bloch spaces in the polydisc, endpoint results for Hankel operators and pointwise multipliers

本文研究单位多圆盘中的两类对数 Bloch 空间，利用有界 Hankel 算子的符号给出等价刻画，并完整描述不同 Bloch 空间之间的逐点乘子。