分形上的分析及其应用
基本信息
结项摘要
本项目的主要研究内容是分形上的分析，具体的是分形上的函数空间和分形上的调和分析。. 在距离空间上定义函数空间，主要是Sobolev型空间是近期比较热门的研究方向，国际上已有许多人从不同的角度定义了多中距离空间上的Sobolev型空间,我们将通过在距离空间中定义的Lipschitz型空间,研究其与其他类型的距离空间上的Sobolev型空间的关系，主要是与Hazlasz型的Sobolev型空间的关系，并进而研究在这些空间上的Sobolev和Poincare型不等式。另一方面我们将对自相似测度的Fourier变换的性质做进一步的研究，一般的球面自相似测度的最大模算子的有界性问题如Cantor测度的最大模算子的有界性问题仍是一个未解决的问题，我们希望在这问题上有所收获。
项目摘要
项目成果
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数据更新时间：2023-05-31
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林勇的其他基金
相似国自然基金
分形、图和距离空间上的分析及其应用
某些分形集上的调和分析
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支撑在分形集上的测度分析