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Good λ inequalities for nontangential maximal functions and S-functions of harmonic functions

  • Akihito Uchiyama
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

For a harmonic function u(x, t) on R+n+1, let Nδu be as in (0.2) and let
$$ \begin{gathered} S_\delta \left( {t\left| {\nabla _u } \right|} \right)\left( x \right) \hfill \\ = \left\{ {\Gamma \left( {\frac{{n + 2}} {2}} \right)\pi ^{ - n/2} \smallint \smallint _{\Gamma \left( {x,\delta } \right)} t^2 \left| {\nabla u\left( {y,t} \right)} \right|^2 \left( {\delta t} \right)^{ - n} dydt/t} \right\}^{1/2} , \hfill \\ \end{gathered} $$
where ∇ = (Dt,D X1,…,D Xn). We will show the following precise relations between Nδu and Sδ (t|∇u|).

Keywords

Distribution Function Euclidean Space Harmonic Function Number Theory Geometric Property 
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 Japan 2001

Authors and Affiliations

  • Akihito Uchiyama

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