Regularities of Time-Fractional Derivatives of Semigroups Related to Schrodinger Operators with Application to Hardy-Sobolev Spaces on Heisenberg Groups
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In this paper, assume that L=−Δℍn+V is a Schrödinger operator on the Heisenberg group ℍn, where the nonnegative potential V belongs to the reverse Hölder class BQ/2. By the aid of the subordinate formula, we investigate the regularity properties of the time-fractional derivatives of semigroups e−tLt>0 and e−tLt>0, respectively. As applications, using fractional square functions, we characterize the Hardy-Sobolev type space HL1,αℍn associated with L. Moreover, the fractional square function characterizations indicate an equivalence relation of two classes of Hardy-Sobolev spaces related with L.
2005 ◽
Vol 3
(2)
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pp. 183-208
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2014 ◽
Vol 2014
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pp. 1-7
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2012 ◽
Vol 164
(11)
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pp. 1501-1512
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2017 ◽
Vol 54
(2)
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pp. 205-220
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