论文标题
Lorentz规范的离散化和反策划，没有对重量的限制
Discretization and antidiscretization of Lorentz norms with no restrictions on weights
论文作者
论文摘要
我们通过消除对所涉及权重的所有“非分类”限制来提高加权洛伦兹规范的离散技术。我们使用新方法来提供对最佳常数$ c $的等效估计，使得不等式$$ \ left（\ int_0^l（f^*（t））^{p_2} w（t） u（s）\，\ mathrm {d} s \ right）^{ - \ frac {p_1}α} \ left（\ int_0^t（\ int_0^t（f^*（s））^αu（s）\，\ s） \right)^\frac 1{p_1}$$ holds for all relevant measurable functions, where $L\in(0,\infty]$, $α, p_1, p_2 \in (0,\infty)$ and $u$, $v$, $w$ are locally integrable weights, $u$ being strictly positive. It the case of weights that would be otherwise excluded by the restrictions, it表明，还出现了$ p_1 = \ infty $的弱类似物的特征中的其他限制术语。
We improve the discretization technique for weighted Lorentz norms by eliminating all "non-degeneracy" restrictions on the involved weights. We use the new method to provide equivalent estimates on the optimal constant $C$ such that the inequality $$\left( \int_0^L (f^*(t))^{p_2} w(t)\,\mathrm{d}t \right)^\frac 1{p_2} \le C \left( \int_0^L \left( \int_0^t u(s)\,\mathrm{d}s \right)^{-\frac {p_1}α} \left( \int_0^t (f^*(s))^αu(s) \,\mathrm{d}s \right)^\frac {p_1}αv(t) \,\mathrm{d}t \right)^\frac 1{p_1}$$ holds for all relevant measurable functions, where $L\in(0,\infty]$, $α, p_1, p_2 \in (0,\infty)$ and $u$, $v$, $w$ are locally integrable weights, $u$ being strictly positive. It the case of weights that would be otherwise excluded by the restrictions, it is shown that additional limit terms naturally appear in the characterizations of the optimal $C$. A weak analogue for $p_1=\infty$ is also presented.
