论文标题
广义功能的临界平滑度
The Critical Smoothness of Generalized Functions
论文作者
论文摘要
对于每个集成性参数$ p \ in（0，\ infty] $，定期广义函数$ f $的关键平滑度，由$ s_f（p）$表示是$ f $ f $ s $ f $属于besov space $ b_ b_ b_ b_ p，p，p，p} s $（或其他类似函数）的clifteration的$ f $ s $ s $ s $ s $ s $ s $ s $ s primate vartility actution的临时效果的临时。 $ p $。当$ f $描述了广义周期性功能的空间时，我们的主要结果是所有可能的关键平滑度功能$ p \ mapsto s_f（p）$。
For each integrability parameter $p \in (0,\infty]$, the critical smoothness of a periodic generalized function $f$, denoted by $s_f(p)$ is the supremum over the smoothness parameters $s$ for which $f$ belongs to the Besov space $B_{p,p}^s$ (or other similar function spaces). This paper investigates the evolution of the critical smoothness with respect to the integrability parameter $p$. Our main result is a simple characterization of all the possible critical smoothness functions $p\mapsto s_f(p)$ when $f$ describes the space of generalized periodic functions. We moreover characterize the compressibility of generalized periodic functions in wavelet bases from the knowledge of their critical smoothness function.
