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Pointwise Estimates for Integral Kernels

  • Fritz Gesztesy
  • Marcus Waurick
Chapter
  • 484 Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 2157)

Abstract

This chapter focuses on pointwise estimates as well as regularity properties of various integral kernels of the integral operators discussed in the previous Chap.  4 We particularly derive estimates for integral operators induced by certain commutators. This chapter concludes with series representations and estimates of the resolvent kernel (essentially, a Hankel function of the first kind) of the Laplacian in \(L^{2}(\mathbb{R}^{n})\).

Keywords

Integral Kernel Obtain Pointwise Estimates Resolvent Kernel Helmholtz Green's Function Sobolev Scale 
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References

  1. 1.
    M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972)Google Scholar
  2. 2.
    R.A. Adams, J.J.F. Fournier, Sobolev spaces, 2nd edn. (Academic Press, New York, 2003)Google Scholar
  3. 57.
    I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products, corrected and enlarged edition, prepared by A. Jeffrey (Academic Press, San Diego, 1980)Google Scholar
  4. 96.
    H. Triebel, Interpolation Theory, Function Spaces, Differential Operators (North-Holland, Amsterdam, 1978)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Fritz Gesztesy
    • 1
  • Marcus Waurick
    • 2
  1. 1.Dept of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Institut für AnalysisTU DresdenDresdenGermany

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