论文标题
一类从勒布斯格空间到谐波伯格曼 - 巴索夫或加权的Bloch空间的整体运营商
A class of Integral Operators from Lebesgue spaces into Harmonic Bergman-Besov or Weighted Bloch Spaces
论文作者
论文摘要
我们考虑由$ \ Mathbb {r}^{n} $在单位球上引起的一类两参数加权积分运算符，并精确地表征了从lebesgue space $ l^{p}_α$中限制的那些，并精确地表征了那些从lebesgue space中限制的。 $ b^{\ infty}_β$，以$ 1 \ leq p \ leq \ infty $，$ 1 \ leq q <\ infty $和$α，β\ in \ mathbb {r} $。这些操作员可以看作是谐波伯格曼 - 贝索夫预测的概括。另外，我们的结果消除了令人不安的条件$β> -1 $当$ q <\ infty $和$β\ geq 0 $当$ q = \ infty $ ofdoğan（由雷伯斯格类上的谐波伯格曼 - 贝斯夫（Harmonic Bergman-Besov）诱发的一类积分运算符，preprint，preprint，2020，2020年），通过将这些space类代替这些space类映射到lebesgue。
We consider a class of two-parameter weighted integral operators induced by harmonic Bergman-Besov kernels on the unit ball of $\mathbb{R}^{n}$ and characterize precisely those that are bounded from Lebesgue spaces $L^{p}_α$ into Harmonic Bergman-Besov $b^{q}_β$ or weighted Bloch Spaces $b^{\infty}_β $, for $1\leq p\leq\infty$, $1\leq q< \infty$ and $α,β\in \mathbb{R}$. These operators can be viewed as generalizations of the harmonic Bergman-Besov projections. Also, our results remove the disturbing conditions $β>-1$ when $q<\infty$ and $β\geq 0$ when $q=\infty$ of Doğan (A Class of Integral Operators Induced by Harmonic Bergman-Besov kernels on Lebesgue Classes, preprint, 2020) by mapping the operators into these spaces instead of the Lebesgue classes.
