| Authors: | Stević, Stevo | Title: | A Littlewood-Paley type inequality | Journal: | Bulletin of the Brazilian Mathematical Society | Volume: | 34 | Issue: | 2 | First page: | 211 | Last page: | 217 | Issue Date: | 1-Jul-2003 | Rank: | M23 | ISSN: | 1678-7544 | DOI: | 10.1007/s00574-003-0008-1 | Abstract: | In this note we prove the following theorem: Let u be a harmonic function in the unit ball B ⊂ Rn and p ∈ [n-2/n-1, 1]. Then there is a constant C = C(p,n) such that sup0≤r≤1∫ s|u(rζ)|pdσ(ζ) ≤ C (|u(0)|p + ∫B|∇u(x)|p(1 - |x|)p-1dV(x). |
Keywords: | Hardy space | Harmonic functions | Littlewood-Paley inequality | Maximal function | Unit ball | Publisher: | Springer Link |
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