论文标题
运营商可以将$ ul^\ infty $映射到$ {\ rm {bmo}} _ U $的足够条件
A Sufficient Condition For An Operator To Map $uL^\infty$ to ${\rm{BMO}}_u$
论文作者
论文摘要
令$ t $为操作员，并假设存在一个正常数$ c $，以便$$ \ weft（\ int_i | tf（x）|^q \，dx \ right）^{1/q} \ leq c \ leq c \ left（\ int_i | f（x） $ i $ in $ \ mathbb {r} $和l^{\ infty}（\ mathbb {r}）$中的$ f \ in $ f \。然后，我们表明$ t $ maps $ ul^{\ infty} $ to $ {\ rm {bmo}} _ U $。
Let $T$ be an operator and suppose that there exists a positive constant $C$ such that $$\left(\int_I|Tf(x)|^q\, dx\right)^{1/q}\leq C\left(\int_I|f(x)|^q\, dx\right)^{1/q}$$ for every $q$ which is near enough to $1$ and for every interval $I$ in $\mathbb{R}$ and $f\in L^{\infty}(\mathbb{R})$. Then we show that $T$ maps $uL^{\infty}$ to ${\rm{BMO}}_u$.
