论文标题
Sobolev和Hölder估计$ \ overline \ partial $ - equipation的同型操作员的估计有限multunite的\ partial $ - equigation
Sobolev and Hölder estimates for homotopy operators of the $\overline\partial$-equation on convex domains of finite multitype
论文作者
论文摘要
我们为具有最佳Sobolev和Hölder估计的有限类型的凸域上的$ \ overline \ partial $ - 方程构建同型公式。对于具有$ q $ -type $ type $ m_q $的有限光滑有限型凸域$ω\ subset \ mathbb c^n $，$ 1 \ le q \ le q \ le n $，我们的$ \ operline \ partial \ partial $ solutial $ solutial $ $ \ solutia h_q：h^{s，p} \ to h^{s+1/m_q，p} $和hölder-zygmund有限额$ \ mathcal h_q：\ Mathscr c^s \ to \ Mathscr c^{s s+1/m_q} $ for All $ s $ s $ in \ math $ p <我们还向全部$ s \ in \ mathbb r $和$ 1 <p <r_q $，$ l^p $ bundedness $ \ mathcal h_q：h^{s，p} \ to H^{
We construct homotopy formulas for the $\overline\partial$-equation on convex domains of finite type that have optimal Sobolev and Hölder estimates. For a bounded smooth finite type convex domain $Ω\subset\mathbb C^n$ that has $q$-type $m_q$ for $1\le q\le n$, our $\overline\partial$ solution operator $\mathcal H_q$ on $(0,q)$-forms has (fractional) Sobolev boundedness $\mathcal H_q:H^{s,p}\to H^{s+1/m_q,p}$ and Hölder-Zygmund boundedness $\mathcal H_q:\mathscr C^s\to\mathscr C^{s+1/m_q}$ for all $s\in\mathbb R$ and $1<p<\infty$. We also show the $L^p$-boundedness $\mathcal H_q:H^{s,p}\to H^{s,pr_q/(r_q-p)}$ for all $s\in\mathbb R$ and $1<p<r_q$, where $r_q:=(n-q+1)m_q+2q$.
