Estimates in Lp for magnetic Schrödinger operators

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44 Scopus citations


We study the magnetic Schrödinger operator H(a,V) in ℝn, n ≥ 3. The Lp (1 < p < ∞) and weak-type (1,1) estimates are obtained under certain conditions, given in terms of the reverse Hölder inequality, on the magnetic field B = curl a and the electrical potential V. In particular, we show that the Lp and weak-type (1,1) estimates hold if the components of a are polynomials, and V is a nonnegative polynomial.

Original languageEnglish
Pages (from-to)817-841
Number of pages25
JournalIndiana University Mathematics Journal
Issue number3
StatePublished - 1996

ASJC Scopus subject areas

  • Mathematics (all)


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