论文标题
在多型环境中的空间和Frisch-Parisi猜想
Besov spaces in multifractal environment and the Frisch-Parisi conjecture
论文作者
论文摘要
在本文中，提出了一种解决所谓的弗里希·帕里斯（Frisch-Parisi）猜想的解决方案。这项成就基于本文开发的三种成分。首先构建了$ \ r^d $上的完全支持的ra，并建立了规定的奇异性光谱。其次，我们定义新的\ textit {异质} besov spaces $ b^{μ，p} _ {q} $，并使用小波系数找到表征。最后，我们充分描述了函数空间中典型函数的多重性质，$ b^{μ，p} _ {q} $。结合了这三个结果，我们发现了Baire功能空间，其中典型功能具有规定的奇异性光谱并满足多重形式主义。这给出了Frisch-Parisi猜想的答案。
In this article, a solution to the so-called Frisch-Parisi conjecture is brought. This achievement is based on three ingredients developed in this paper. First almost-doubling fully supported Radon measures on $\R^d$ with a prescribed singularity spectrum are constructed. Second we define new \textit{heterogeneous} Besov spaces $B^{μ,p}_{q}$ and find a characterization using wavelet coefficients. Finally, we fully describe the multifractal nature of typical functions in the function spaces $B^{μ,p}_{q}$. Combining these three results, we find Baire function spaces in which typical functions have a prescribed singularity spectrum and satisfy a multifractal formalism. This yields an answer to the Frisch-Parisi conjecture.
