Một Giới Hạn Trên Của Độ Dimension Hausdorff Của Tập Phân Kỳ Của Toán Tử Schrödinger Phân Số Trên Hs(ℝn)

Acta Mathematica Scientia - Tập 41 - Trang 1223-1249 - 2021
Dan Li1, Junfeng Li2, Jie Xiao3
1School of Mathematics and Statistics, Beijing Technology and Business University, Beijing, China
2School of Mathematical Sciences, Dalian University of Technology, Dalian, China
3Department of Mathematics and Statistics, Memorial University, St. John’s, Canada

Tóm tắt

Cho n ≥ 2 và \(\alpha > \tfrac{1}{2}\), chúng tôi đã đạt được một giới hạn trên cải thiện của độ dimension Hausdorff của toán tử Schrödinger phân số; tức là, \(\mathop {\sup }\limits_{f \in {H^s}({\mathbb{R}^n})} {\dim _H}\left\{ {x \in {{\mathbb{R}^n}}:\;\mathop {\lim }\limits_{t \to 0} {e^{{\rm{i}}t{{( - \Delta )}^\alpha }}}f(x) \ne f(x)} \right\} \le n + 1 - {{2(n + 1)s} \over n}\) cho \(\tfrac{n}{{2(n + 1)}} < s \le \tfrac{n}{2}\).

Từ khóa


Tài liệu tham khảo

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