论文标题
$ \ mathbb {r}^2 $的lojasiewicz不平等
A Lojasiewicz Inequality in Hypocomplex Structures of $\mathbb{R}^2$
论文作者
论文摘要
For a real analytic complex vector field $L$ in an open set of $\mathbb{R}^2$, with local first integrals that are open maps, we attach a number $μ\ge 1$ (obtained through Lojasiewicz inequalities) and show that the equation $Lu=f$ has bounded solutions when $f\in L^p$ with $p>1+μ$.我们还建立了方程$ lu = au+b \ overline {u} $（带有$ a，b \ in l^p $）的有限解决方案和holomorphic函数之间的相似性原理。
For a real analytic complex vector field $L$ in an open set of $\mathbb{R}^2$, with local first integrals that are open maps, we attach a number $μ\ge 1$ (obtained through Lojasiewicz inequalities) and show that the equation $Lu=f$ has bounded solutions when $f\in L^p$ with $p>1+μ$. We also establish a similarity principle between the bounded solutions of the equation $Lu=Au+B\overline{u}$ (with $A,B\in L^p$) and holomorphic functions.
