论文标题
关于振荡最大功能的终点行为
On the endpoint behaviour of oscillatory maximal function
论文作者
论文摘要
受谎言问题的启发，我们研究了振荡性最大函数的$ l^1（\ mathbb {r}）$的子空间的界限。特别是，我们在$ l^1（\ mathbb {r}）$中构建功能，这些功能永远无法在我们的最大函数的行动下集成。另一方面，我们证明这些最大功能将某些类似于Sobolev空间的空间映射到$ l^1（\ Mathbb {r}）$在相位$γ$上的温和曲率假设下连续地连续地。
Inspired by a question of Lie, we study boundedness in subspaces of $L^1(\mathbb{R})$ of oscillatory maximal functions. In particular, we construct functions in $L^1(\mathbb{R})$ which are never integrable under action of our class of maximal functions. On the other hand, we prove that these maximal functions map certain classes of spaces resembling Sobolev spaces into $L^1(\mathbb{R})$ continuously under mild curvature assumptions on the phase $γ$.
