论文标题
$ \ mathbb {r}^\ infty $和bessel势
HK-Sobolev space $W{S^{k,p}}$ on $\mathbb{R}^\infty$ and Bessel Potential
论文作者
论文摘要
我们在本文中的目标是在$ \ r^\ infty $上构建HK-Sobolev空间，其中包含Sobolev空间作为密集的嵌入。我们讨论Sobolev空间弱解的序列在HK-Sobolev空间中强烈收敛。同样，我们获得了通过贝塞尔电势的Sobolev空间密集地包含在HK-Sobolev空间中。最后，我们找到了足够的条件，可以解决差异方程$ \ nabla.f = f，$ f $的$是子空间$ k {s^p} [\ r_i^n] $和$ n \ in \ n $的$ k {s^p}，在sobohk-sobolev space $ ws $ ws $ ws $ ws^{
Our goal in this article is to construct HK-Sobolev spaces on $\R^\infty$ which contains Sobolev spaces as dense embedding. We discuss that the sequence of weak solution of Sobolev spaces are convergence strongly in HK-Sobolev space. Also, we obtain that the Sobolev space through Bessel Potential is densely contained in HK-Sobolev spaces. Finally we find sufficient condition for the solvability of the divergence equation $\nabla.F= f,$ for $f$ is an element of the subspace $K{S^p}[\R_I^n]$ and $n \in \N$, in the SoboHK-Sobolev space $WS^{k,p}[\R_I^n] $ with the help of Fourier transformation.
