论文标题
根据Sobolev空间规律性的多线性乘数表征
Characterization of multilinear multipliers in terms of Sobolev space regularity
论文作者
论文摘要
我们为多连线乘数运算符提供了必要的条件，并在所有annuli上均匀地均匀地使用$ l^r $的产品类型的sobolev空间，以从耐力空间的产品到lebesgue空间。我们考虑了$ 1 <r \ leq 2 $的情况，并且我们以与Lebesgue索引（或Hardy指数），维度以及Sobolev空间的规则性和集成性指数有关的不平等来表征有限性。 Case $ r> 2 $无法通过已知技术来处理，并且保持开放。我们的结果不仅扩展了，而且还建立了宫丘，Nguyen，Tomita和第一作者的先前结果的清晰度，他们仅考虑了$ r = 2 $。
We provide necessary and sufficient conditions for multilinear multiplier operators with symbols in $L^r$-based product-type Sobolev spaces uniformly over all annuli to be bounded from products of Hardy spaces to a Lebesgue space. We consider the case $1<r\leq 2$ and we characterize boundedness in terms of inequalities relating the Lebesgue indices (or Hardy indices), the dimension, and the regularity and integrability indices of the Sobolev space. The case $r>2$ cannot be handled by known techniques and remains open. Our result not only extends but also establishes the sharpness of previous results of Miyachi, Nguyen, Tomita, and the first author, who only considered the case $r=2$.
