论文标题
Lebesgue课程的Harmonic Bergman-Besov内核引起的一类积分运营商
A Class of Integral Operators Induced by Harmonic Bergman-Besov kernels on Lebesgue Classes
论文作者
论文摘要
我们根据六个参数提供了一个完整的表征，涉及所有标准加权积分算子的界限，这些积分算子由谐波伯格曼 - 贝索夫核引起的所有标准的bergman-besov内核作用在不同的lebesgue类之间，在r^{n}的单位球上具有标准权重。这些操作员在某种意义上概括了Harmonic Bergman-Besov的预测。为了获得必要条件，我们使用的技术在很大程度上取决于谐波伯格曼 - 贝索夫与装置球上的加权Bloch空间之间的精确包含关系。这种富有成果的技术是新的。它首先与Kaptanoğlu和üreyen的Holomorthic Bergman-Besov内核一起使用。我们采用的充分证明方法是Schur测试或Hölder或Minkowski型不平等现象，这些不平等现象也利用了诸如鲁丁类型积分的估计值。
We provide a full characterization in terms of the six parameters involved the boundedness of all standard weighted integral operators induced by harmonic Bergman-Besov kernels acting between different Lebesgue classes with standard weights on the unit ball of R^{n}. These operators in some sense generalize the harmonic Bergman-Besov projections. To obtain the necessity conditions, we use a technique that heavily depends on the precise inclusion relations between harmonic Bergman-Besov and weighted Bloch spaces on the unit ball. This fruitful technique is new. It has been used first with holomorphic Bergman-Besov kernels by Kaptanoğlu and Üreyen. Methods of the sufficiency proofs we employ are Schur tests or Hölder or Minkowski type inequalities which also make use of estimates of Forelli-Rudin type integrals.
