Skip to main content
SpringerLink
Log in
Book cover

The Maz’ya Anniversary Collection pp 345–352Cite as

Birkhäuser

A Remark on Hardy type inequalities for critical Schrödinger operators with magnetic fields

  • Conference paper

  • 682 Accesses

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 110))

Abstract

We prove that the inclusion of a non-trivial magnetic field into a critical Schrödinger operator always removes the criticality and implies a corresponding Hardy type inequality.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Y. Avron, I. Herbst, B. Simon: “Schrödinger Operators with Magnetic Fields I”, Duke Math J, 45 (1978) 847–883.

    Article  MathSciNet  MATH  Google Scholar 

  2. M.Sh. Birman, G.D. Raikov: “Discrete Spectrum in the Gaps for Perturbations of the Magnetic Schrödinger Operator”, Adv. Sov. Math. 7 (1991) 75–84.

    MathSciNet  Google Scholar 

  3. B. Helffer: “Semi-classical Analysis for the Schrödinger Operator and Applications”, Lecture Notes in Mathematics 1336, Springer-Verlag, 1998, vi+107 pp.

    Google Scholar 

  4. T. Kato: “Schrödinger Operators with singular Potentials”, Israel J Math, 13 (1972) 135–148.

    Article  MathSciNet  Google Scholar 

  5. A. Laptev, T. Weidl: “Hardy inequalities for magnetic Dirichlet forms”, Preprint.

    Google Scholar 

  6. V.G. Mazja: Sobolev Spaces. Springer Series in Soviet Mathematics. Springer-Verlag, Berlin-New York, 1985.

    Google Scholar 

  7. G. Rozenblum, M.Z. Solomyak: “On Principal Eigenvalues for Indefinite Problems in the Euclidean Space”, Math Nachr 192 (1998) 205–223.

    Article  MathSciNet  MATH  Google Scholar 

  8. T. Weidl: “Remarks on virtual bound states for semi-bounded operators”, Comm Partial Diff Eq 241&2 (1999) 25–60.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, S-10044, Stockholm, Sweden

    Timo Weidl

  2. Universität Regensburg, Naturwissenschaftliche Fakultät I, D-93040, Regensburg, Germany

    Timo Weidl

Authors
  1. Timo Weidl
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Rostock, D-18051, Rostock, Germany

    Jürgen Rossmann , Peter Takáč  & Günther Wildenhain ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Basel AG

About this paper

Cite this paper

Weidl, T. (1999). A Remark on Hardy type inequalities for critical Schrödinger operators with magnetic fields. In: Rossmann, J., Takáč, P., Wildenhain, G. (eds) The Maz’ya Anniversary Collection. Operator Theory: Advances and Applications, vol 110. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8672-7_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8672-7_19

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9725-9

  • Online ISBN: 978-3-0348-8672-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation