schrÖdinger最大算子的估计——复杂时间长曲线

Pub Date : 2020-01-01 DOI:10.4134/JKMS.J180558

Yao-ming Niu, Ying Xue

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引用次数: 2

摘要

．本文给出了算子P ta，γ f (cid:0) Γ(x,t) (cid:1)沿复时间曲线的l2极大估计的一些刻画，该曲线定义为t，γ > 0和a≥2，曲线Γ是满足Γ: R x[0,1]→R的函数，满足H¨older的阶σ条件和bilipschitz条件。作者将Bailey[1]和Cho, Lee和Vargas[3]的复时Schr¨odinger型的结果推广到沿曲线的Schr¨odinger算子。

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ESTIMATES FOR SCHRÖDINGER MAXIMAL OPERATORSALONG CURVE WITH COMPLEX TIME

. In the present paper, we give some characterization of the L 2 maximal estimate for the operator P ta,γ f (cid:0) Γ( x,t ) (cid:1) along curve with complex time, which is deﬁned by where t,γ > 0 and a ≥ 2 , curve Γ is a function such that Γ : R × [0 , 1] → R , and satisﬁes H¨older’s condition of order σ and bilipschitz conditions. The authors extend the results of the Schr¨odinger type with complex time of Bailey [1] and Cho, Lee and Vargas [3] to Schr¨odinger operators along the curves.

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