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Potentials on RN

  • David E. Edmunds
  • Vakhtang Kokilashvili
  • Alexander Meskhi
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 543)

Abstract

In this chapter we develop a new approach to truncated potentials. We introduce the extension of truncated potentials and prove necessary and sufficient conditions for boundedness from L p (R n ) into L v q (R n ), when 1 < p < ∞, 0 < q < ∞ and α > n/p. A generalization of Sawyer’s result [258] is presented. Then a compactness criterion for this operator is proved, and upper and lower estimates of its distance from the class of compact operators are derived.

Keywords

Compact Operator Riesz Potential Positive Borel Measure Radial Kernel Weak Type Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • David E. Edmunds
    • 1
  • Vakhtang Kokilashvili
    • 1
  • Alexander Meskhi
    • 2
  1. 1.Centre for Mathematical Analysis and its ApplicationUniversity of SussexSussexUK
  2. 2.A. Razmadze Mathematical InstituteGeorgian Academy of SciencesTbilisiGeorgia

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