算子值傅里叶乘子与向量值边值问题最大正则性

Operator-valued Fourier Multipliers and Maximal Regularity for Vector-valued Boundary Problems

向量值LP空间上的算子值傅里叶乘子由于L.Weis在2000年的重要工作而成为泛函分析的热点之一,其对R-有界性创造性的应用使这个领域的研究耳目一新,新的结果层出不穷.本文的目的是介绍算子值傅里叶乘子的这些最新进展, 以及它们在向量值边值问题最大正则性方面的应用.包括N.J.Kalton和G.Lancien给出的关于Lp-最大正则性的反例. Besov空间和Triebel空间上的算子值傅里叶乘子以及在Besov空间和.Triebel空间意义下的最大正则性也是我们要介绍的内容.

Operator-valued Fourier multipliers on vector-valued Lp spaces have been extensively studied since the important contribution of L. Weis in 2000. The most important tool used by L. Weis is the so called .R-boundedness for sets of operators. In this survey, we will give new results in this direction obtained in the last four years, and its applications in the study of maximal regularity in the Lp sense for vector-valued boundary problems, this include the counter-example given by N. J. Kalton and G. Lancien. We will also give the corresponding results in the case of Besov spaces and Triebel spaces, and the corresponding results of maximal regularity in theses function spaces.