Sharp decay estimates of L^q norms of nonnegative Schroedinger heat semigroups
Sharp decay estimates of L^q norms of nonnegative Schroedinger heat semigroups
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非负薛定谔热半群的 L^q 范数的急剧衰减估计
DOI：
10.1016/j.jfa.2013.03.009
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Kazuhiro Ishige and Eiji Yanagida
中科院分区：
文献类型：
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作者：
Norisuke Ioku;Kazuhiro Ishige and Eiji Yanagida
设H=−Δ+V是L2（RN）上的非负薛定谔算子，其中N ≠ 3，V是RN中在无穷远处二次衰减的径向对称非正函数。对于任意1 <$p <$q <$∞，我们用<$e−tH <$q，p表示薛定谔热半群e− tH从Lp（RN）到Lq（RN）的算子范数。本文在V上适当的条件下，给出了对所有1 <$p <$q <$∞，ε e−tH <$q，pas t→∞的精确和最优衰减率. <$e−tH <$q，p的衰变率取决于算子H是次临界的还是临界的，以及算子H的正调和函数的行为。
Let H=−Δ+V be a nonnegative Schrödinger operator on L2(RN), where N⩾3 and V is a radially symmetric nonpositive function in RNdecaying quadratically at the space infinity. For any 1⩽p⩽q⩽∞, we denote by ‖e−tH‖q,pthe operator norm of the Schrödinger heat semigroup e−tHfrom Lp(RN) to Lq(RN). In this paper, under suitable conditions on V, we give the exact and optimal decay rates of ‖e−tH‖q,pas t→∞ for all 1⩽p⩽q⩽∞. The decay rates of ‖e−tH‖q,pdepend on whether the operator H is subcritical or critical and on the behavior of the positive harmonic function for the operator H.