Riesz Transforms Associated with Higher-Order Schrödinger Type Operators
Riesz Transforms Associated with Higher-Order Schrödinger Type Operators
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DOI：
10.1007/s11118-017-9661-7
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发表时间：
2016-03
影响因子：
1.1
通讯作者：
Qingquan Deng;Yong Ding;X. Yao
中科院分区：
文献类型：
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作者：
Qingquan Deng;Yong Ding;X. Yao
设L =L0+ V是薛定谔型算子，其中L0是具有有界复系数的高阶椭圆算子，V是符号可测函数.在V的强次临界假设下，基于半群−tL的非对角估计，研究了Riesz变换<$mL−1/2（q ≤ 2）的Lq有界性.此外，作者对V施加了额外的正则性假设，以获得Riesz变换的Lq有界性，其中some q> 2。特别地，这些结果被应用到更有趣的薛定谔算子L =P（D）+V，其中P（D）是任何具有常系数的齐次正椭圆算子。
LetL=L0+Vbe a Schrödinger type operator, whereL0is a higher order elliptic operator with bounded complex coefficients in divergence form andVis a signed measurable function. Under the strongly subcritical assumption onV, we study theLqboundedness of Riesz transform ∇mL−1/2forq≤ 2 based on the off-diagonal estimates of semigroupe−tL. Furthermore, the authors impose extra regularity assumptions onVto obtain theLqboundedness of Riesz transform ∇mL−1/2for someq> 2. In particular, these results are applied to the more interesting Schrödinger operatorsL=P(D) +V, whereP(D) is any homogeneous positive elliptic operator with constant coefficients.