Pointwise inequalities of logarithmic type in Hardy-Hölder spaces
We prove some optimal logarithmic estimates in the Hardy space with Hölder regularity, where is the open unit disk or an annular domain of . These estimates extend the results established by S. Chaabane and I. Feki in the Hardy-Sobolev space 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 for Hölder functions. As an application of these estimates, we study the stability of both the Cauchy problem...