论文标题
平均差异差异的差异不平等
Variational Inequalities For The Differences Of Averages Over Lacunary Sequences
论文作者
论文摘要
令$ f $为$ \ mathbb {r} $上定义的本地集成函数，让$（n_k）$为eacunary序列。定义操作员$ a_ {n_k} $ by $$ a_ {n_k} f（x）= \ frac {1} {n_k} \ int_0^{n_k} f（x-t） $$ \ MATHCAL {V} _sf（x）= \ left（\ sum_ {k = 1}^\ infty | a_ {n_k} f（x）f（x）-a_ {n_ {k-1}} f（k-1}} f（x）f（x）
Let $f$ be a locally integrable function defined on $\mathbb{R}$, and let $(n_k)$ be a lacunary sequence. Define the operator $A_{n_k}$ by $$A_{n_k}f(x)=\frac{1}{n_k}\int_0^{n_k}f(x-t)\, dt.$$ We prove various types of new inequalities for the variation operator $$\mathcal{V}_sf(x)=\left(\sum_{k=1}^\infty|A_{n_k}f(x)-A_{n_{k-1}}f(x)|^s\right)^{1/s}$$ when $2\leq s<\infty$.
