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We prove some optimal logarithmic estimates in the Hardy space H∞(G) with Hölder regularity, where G is the open unit disk or an annular domain of ℂ. These estimates extend the results established by S.Chaabane and I.Feki in the Hardy-Sobolev space Hk,∞ of the unit disk and those of I. Feki in the case of an annular domain. The proofs are based on a variant of Hardy-Landau-Littlewood inequality...
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