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Journal of Mathematical Sciences

, Volume 169, Issue 2, pp 167–187 | Cite as

Sharp pointwise estimates for directional derivatives of harmonic functions in a multidimensional ball

  • G. Kresin
  • V. Maz’ya
Article

A representation of the sharp constant in a pointwise estimate for the absolute value of the directional derivative of a harmonic function in a multidimensional ball is obtained under the assumption that the boundary values of the function belong to L p . This representation is specified in the cases of radial and tangential derivatives. It is proved for p = 1 and p = 2 that the maximum of the absolute value of the directional derivative of a harmonic function with a fixed L p -norm of its boundary values is attained at the radial direction. This confirms D. Khavinson’s conjecture for p = 1 and p = 2. Bibliography: 11 titles.

Keywords

Harmonic Function Arbitrary Point Directional Derivative Sharp Estimate Hypergeometric Gauss Function 
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, Inc. 2010

Authors and Affiliations

  1. 1.Ariel University Center of SamariaArielIsrael
  2. 2.University of LiverpoolLiverpoolUK
  3. 3.Linköping UniversityLinköpingSweden

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