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- W2364684788 abstract "Let u(z) be a real_valued harmonic function in the unit disk, we say u(z)∈h p(1p+∞), if the p _mean M p(r,u)=12π∫ 2π 0|u(re i θ )| p d θ 1/p is bounded. M.Riesz showed that if u(z)∈h p(1p+∞), then there exists a constant A p, depending only on p such that M p(r,v)≤A pM p(r,u), where v(z) is the conjugate harmonic function of u(z).When v(0)=0 and 1p≤2, W.K.Hayman showed that A p can be given by pp-1 1/p . First, this paper shows that the constant pp-1 1/p can be changed by a smaller constant pp-1 2/p -1 1/2 . Next, if 1p≤2, then there exists a constant θ 0∈2-p2pπ,π2p such that M p p(r,v)≤ Im p sin pπ2+ tg pπ2pM p p(r,u) for any analytic function f(z)=u(z)+ i v(z) in the unit disk, whenever -θ 0 arg f(z)π2." @default.
- W2364684788 created "2016-06-24" @default.
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- W2364684788 date "2002-01-01" @default.
- W2364684788 modified "2023-09-22" @default.
- W2364684788 title "A Remark of M.Riesz Theorem" @default.
- W2364684788 hasPublicationYear "2002" @default.
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