论文标题
具有不同标志的平滑度指数的周期性贝塞尔电势空间的乘数
Multipliers in the scale of periodic Bessel potential spaces with smoothness indices of different signs
论文作者
论文摘要
我们证明了在两个周期性的贝塞尔电势空间之间作用的乘数的一般类型描述结果，该空间定义在$ n $ - 尺寸的圆环（如果它们的平滑度索引具有不同的符号）时。这是通过对线性运算符$ j_s $的定期类似物进行详细检查来完成的，该线性运算符$ j_s $用于定义在整个空间$ \ mathbb {r}^n $的贝塞尔电位空间的规模。我们定义$ j_s $的定期类似物的方法使用了有关广义傅立叶系数的渐近行为以及空间之间自然同构的存在的结果所有$ 2 \cdotπ$ - 来自双schwartz space $ \ mathcal {s}'（\ Mathbb {r}^n）$的定期分布。
We prove a general type description result for the multipliers acting between two periodic Bessel potential spaces, defined on the $n$--dimensional torus, in a case when their smoothness indices are of different signs. This is done through the detailed examination of a periodic analogue of the linear operator $J_s$, which is employed in the definition of the scale of the Bessel potential space defined on the whole space $\mathbb{R}^n$. Our method of defining this periodic analogue of $J_s$ uses the results about an asymptotic behaviour of the generalized Fourier coefficients and existence of a natural homeomorphism between the spaces $\mathcal{D}'(\mathbb{T}^n)$ and $S'_{2 \cdot π}(\mathbb{R}^n)$, where the latter consists of all $2 \cdot π$--periodic distributions from the dual Schwartz space $\mathcal{S}'(\mathbb{R}^n)$.
