Corpus ID: 237940590

Stability of Hardy Littlewood Sobolev Inequality under Bubbling

  title={Stability of Hardy Littlewood Sobolev Inequality under Bubbling},
  author={Shrey Aryan},
In this note we will generalize the results deduced in arXiv:1905.08203 and arXiv:2103.15360 to fractional Sobolev spaces. In particular we will show that for $s\in (0,1)$, $n>2s$ and $\nu\in \mathbb{N}$ there exists constants $\delta = \delta(n,s,\nu)>0$ and $C=C(n,s,\nu)>0$ such that for any function $u\in \dot{H}^s(\mathbb{R}^n)$ satisfying, \begin{align*} \left\| u-\sum_{i=1}^{\nu} \tilde{U}_{i}\right\|_{\dot{H}^s} \leq \delta \end{align*} where $\tilde{U}_{1}, \tilde{U}_{2},\cdots \tilde{U… Expand


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    Release 1.1.2 of 2021-06-15