Mathematical Sciences: Applications of Transference in Multiplier Theory

阿斯马尔教授的研究项目涉及迁移方法在分析中的应用。重点是寻找极大算子和其他奇异积分算子的强弱型范数的无关界。所研究的方法和应用涉及无限维空间中的算子或函数的种类，这些算子或函数出现在数学物理的偏微分方程组的分析中。例如，这包括电磁学和流体动力学方程。了解这些是有界运算符通常是研究这些方程的解的重要第一步。

Professor Asmar's research project concerns the applications of transference methods in analysis. The emphasis is on finding dimension independent bounds on the strong and weak type norms of maximal operators and other singular integral operators. The method and applications under study involve the kinds of operators or functions in infinite dimensional spaces which occur in the analysis of the partial differential equations of mathematical physics. This includes, for example, the equations of electromagnetism and fluid dynamics. Knowing that these are bounded operators is often an important first step in studying solutions to these equations.