Hardy-Littlewood-Fefferman-Stein type inequalities, 1

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


Theorem 6.A . Let m ∈ {2,3,4, …} and q > 0. Let u (z) be a harmonic function defined on the unit ball of R m. Then
$$ \left| {u\left( 0 \right)} \right|^q \le C\left( {q,m} \right)\smallint _{\left\{ {z \in {\rm{R}}^m :\left| z \right| < 1} \right\}} \left| {u\left( z \right)} \right|^q dz. $$


Euclidean Space Harmonic Function Measurable Function Number Theory Unit Ball 
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© Springer Japan 2001

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  • Akihito Uchiyama

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