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Commutators of Singular Integral Operators Related to Magnetic Schrödinger Operators

Commutators of Singular Integral Operators Related to Magnetic Schrödinger Operators

Year:    2018

Analysis in Theory and Applications, Vol. 34 (2018), Iss. 1 : pp. 45–76

Abstract

Let A:=(ia)·(ia)+V be a magnetic Schrödinger operator on L2(Rn), n2, where a:=(a1,···,an)L2loc(Rn,Rn) and 0VL1loc(Rn). In this paper, we show that for a function b in Lipschitz space Lipα (Rn) with α(0,1), the commutator [b,V1/2A1/2] is bounded from Lp(Rn) to Lq(Rn), where p, q(1,2] and 1/p1/q=α/n

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2018.v34.n1.4

Analysis in Theory and Applications, Vol. 34 (2018), Iss. 1 : pp. 45–76

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    32

Keywords:    Commutator Lipschitz space the sharp maxical function magnetic Schrödinger operator Hölder inequality.