Haar投影数与索伯列夫空间中无条件收敛的失败
Haar projection numbers and failure of unconditional convergence in Sobolev spaces
摘要：
对于$1<p<\infty$，我们确定了$L_p$索伯列夫空间的精确范围，Haar系统是其无条件基。我们还考虑了Triebel-Lizorkin空间的自然扩张，并根据Haar频率集的性质证明了投影算子的范数的上界和下界。
英文摘要：
For $1<p<\infty$ we determine the precise range of $L_p$ Sobolev spaces for which the Haar system is an unconditional basis. We also consider the natural extensions to Triebel-Lizorkin spaces and prove upper and lower bounds for norms of projection operators depending on properties of the Haar frequency set.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
