Factorization and non-factorization theorems for pseudocontinuable functions
英文摘要：
Let $θ$ be an inner function on the unit disk, and let $K^p_θ:=H^p\capθ\overline{H^p_0}$ be the associated star-invariant subspace of the Hardy space $H^p$, with $p\ge1$. While a nontrivial function $f\in K^p_θ$ is never divisible by $θ$, it may have a factor $h$ which is "not too different" from $θ$ in the sense that the ratio $h/θ$ (or just the anti-analytic part thereof) is smooth on the circle. In this case, $f$ is shown to have additional integrability and/or smoothness properties, much in the spirit of the Hardy--Littlewood--Sobolev embedding theorem. The appropriate norm estimates are established, and their sharpness is discussed.
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。
