论文标题
当$αp=（1-κ）n $时
A new estimate for homogeneous fractional integral operators on the weighted Morrey space $L^{p,κ}$ when $αp=(1-κ)n$
论文作者
论文摘要
对于任何$ 0 <α<n $，均质分数积分运算符$ t_ {ω，α} $由\ begin {equation*} t_ {ω{ω，α} f（x）= \ int = \ int _ { r^n} \ frac {ω（x-y）} {| x-y |^{n-α}} f（y）\，dy。 \ end {qore*}在本文中，我们证明，如果$ω$满足$ \ m athbf {s}^{n-1} $上的某些dini平滑条件，则$ t_ {ω，α} $绑定在$ l^{p，κ}（w^p，w^q）$（w^q）$（w^q）$（量）上， $ \ mathrm {bmo}（\ mathbb r^n）$。
For any $0<α<n$, the homogeneous fractional integral operator $T_{Ω,α}$ is defined by \begin{equation*} T_{Ω,α}f(x)=\int_{\mathbb R^n}\frac{Ω(x-y)}{|x-y|^{n-α}}f(y)\,dy. \end{equation*} In this paper, we prove that if $Ω$ satisfies certain Dini smoothness conditions on $\mathbf{S}^{n-1}$, then $T_{Ω,α}$ is bounded from $L^{p,κ}(w^p,w^q)$ (weighted Morrey space) to $\mathrm{BMO}(\mathbb R^n)$.
