论文标题
（CO）凸功能的加权DT-Moduli等效性
Equivalence of Weighted DT-Moduli of (Co)convex Functions
论文作者
论文摘要
该论文提出了加权DT模量的新定义。同样，我们获得了平滑度模量等效的一般结果。众所周知，任何$ r \ in \ mathbb {n} _ {\ circ} $，$ 0 <p \ leq \ infty $，$ 1 \ leqη\ leq r $和$ ϕ（x）= \ sqrt {1-x^2} $ （f^{（r）}，\ |θ_ {\ mathcal {n}} \ |）_ {w_ {w_ {α，β}，p} \ simω^ϕ__ {i，r+1} \; （f^{（R+1）}，\ |θ_ {\ Mathcal {n}} \ |）_ {w_ {w_ {α，β}，p} $和$ω^ϕ__ {i+η} \; （f，\ |θ_ {\ mathcal {n}} \ |）_ {α，β，p} \ sim \ | θ_ {\ Mathcal {n}} \ |^{ - η}ω^ϕ__ {i，2η} \; （f^{（2η）}，\ |θ_ {\ Mathcal {n}} \ |）_ {α+η，β+η，p} $有效。
The paper present new definitions for weighted DT moduli. Similarly, we a general outcome in an equivalence of moduli of smoothness are obtained. It is known that, any $r \in \mathbb{N}_{\circ}$ , $0<p \leq \infty$, $1 \leq η\leq r$ and $ϕ(x)=\sqrt{1-x^2}$, the inequalities $ω^ϕ_{i+1,r} \; (f^{(r)}, \| θ_{\mathcal{N}} \|)_{w_{α, β}, p} \sim ω^ϕ_{i,r+1} \; (f^{(r+1)}, \| θ_{\mathcal{N}} \|)_{w_{α, β}, p}$ and $ω^ϕ_{i+η} \; (f, \| θ_{\mathcal{N}} \|)_{α, β, p} \sim \| θ_{\mathcal{N}} \|^{- η} ω^ϕ_{i, 2 η} \; (f^{(2 η)}, \| θ_{\mathcal{N}} \|)_{α+ η, β+ η, p}$ are valid.
