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Displaying similar documents to “A generalized formula of Hardy.”

Pointwise inequalities of logarithmic type in Hardy-Hölder spaces

Slim Chaabane, Imed Feki (2014)

Czechoslovak Mathematical Journal

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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 H k , ∞ 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...

Growth orders occurring in expansions of Hardy-field solutions of algebraic differential equations

John Shackell (1995)

Annales de l'institut Fourier

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We consider the asymptotic growth of Hardy-field solutions of algebraic differential equations, e.g. solutions with no oscillatory component, and prove that no ‘sub-term’ occurring in a nested expansion of such can tend to zero more rapidly than a fixed rate depending on the order of the differential equation. We also consider series expansions. An example of the results obtained may be stated as follows. Let g be an element of a Hardy field which has an asymptotic series...