Abstract
For \(a \ge - ( \frac{d }{2} - 1)^2 \) and \(2\sigma = {{d - 2}}-( {{{(d - 2)}^2} + 4a})^{1/2}\), let \(\mathcal {\widetilde{H}}_{\sigma }= 2( { - \Delta + \frac{{{\sigma ^2}}}{{{{ | x |}^2}}}})\) be a Schrödinger operator with an inverse-square potential on \( {{\mathbb {R}}^d}\backslash \{0\} \). In this paper, we introduce and investigate the \({{\mathcal {\widetilde{H}}_{\sigma }}}\)-BV capacity, whence discovering some capacitary inequalities on \( \Omega \subseteq {{\mathbb {R}}^d}\backslash \{0\} \).
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Acknowledgements
Y. Liu was supported by the National Natural Science Foundation of China (No. 11671031), the Fundamental Research Funds for the Central Universities (No. FRF-BR-17-004B), and Beijing Municipal Science and Technology Project (No. Z17111000220000). H.H. Wang was supported by Shandong MSTI Project (No. 2019JZZY010122) and MIIT grant (No. J2019-I-0001).
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Communicated by Rosihan M. Ali.
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Yang Han,Yu Liu and Haihui Wang contributed equally to this work.
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Han, Y., Liu, Y. & Wang, H. BV Capacity for the Schrödinger Operator with an Inverse-Square Potential. Bull. Malays. Math. Sci. Soc. 45, 2765–2785 (2022). https://doi.org/10.1007/s40840-022-01358-1
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DOI: https://doi.org/10.1007/s40840-022-01358-1