Displaying similar documents to “Estimates in the Hardy-Sobolev space of the annulus and stability result”

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...

On the Euler function of repdigits

Florian Luca (2008)

Czechoslovak Mathematical Journal

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For a positive integer n we write φ ( n ) for the Euler function of n . In this note, we show that if b > 1 is a fixed positive integer, then the equation φ x b n - 1 b - 1 = y b m - 1 b - 1 , where x , y ∈ { 1 , ... , b - 1 } , has only finitely many positive integer solutions ( x , y , m , n ) .