TY - JOUR
T1 - Fractional Laplacian with Supercritical Killings
AU - Cho, Soobin
AU - Song, Renming
N1 - We thank the two referees for very helpful comments suggestions, particularly for point out the gap in the proof of Lemma 6.2 in the first version. We also thank Panki Kim for helpful comments. Part of the research for this paper was done while the second-named author was visiting Jiangsu Normal University, where he was partially supported by a grant from the National Natural Science Foundation of China (11931004, Yingchao Xie).
Research supported in part by a grant from the Simons Foundation (#960480, Renming Song).
PY - 2025/1
Y1 - 2025/1
N2 - In this paper, we study Feynman-Kac semigroups of symmetric α-stable processes with supercritical killing potentials belonging to a large class of functions containing functions of the form b|x|-β, where b>0 and β>α. We obtain two-sided estimates on the densities p(t, x, y) of these semigroups for all t>0, along with estimates for the corresponding Green functions.
AB - In this paper, we study Feynman-Kac semigroups of symmetric α-stable processes with supercritical killing potentials belonging to a large class of functions containing functions of the form b|x|-β, where b>0 and β>α. We obtain two-sided estimates on the densities p(t, x, y) of these semigroups for all t>0, along with estimates for the corresponding Green functions.
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U2 - 10.1007/s00220-024-05201-5
DO - 10.1007/s00220-024-05201-5
M3 - Article
AN - SCOPUS:85214213267
SN - 0010-3616
VL - 406
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 1
M1 - 22
ER -