### Some integral inequalities of Hardy type

B. Florkiewicz (1980)

Colloquium Mathematicae

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B. Florkiewicz (1980)

Colloquium Mathematicae

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Oguntuase, J.A., Persson, L.-E., Essel, E.K., Popoola, B.A. (2008)

Banach Journal of Mathematical Analysis [electronic only]

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Iwona Skrzypczak (2014)

Banach Center Publications

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We apply general Hardy type inequalities, recently obtained by the author. As a consequence we obtain a family of Hardy-Poincaré inequalities with certain constants, contributing to the question about precise constants in such inequalities posed in [3]. We confirm optimality of some constants obtained in [3] and [8]. Furthermore, we give constants for generalized inequalities with the proof of their optimality.

Alois Kufner (1993)

Collectanea Mathematica

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M. Mateljević, M. Pavlović (1982)

Matematički Vesnik

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Alois Kufner, Lars-Erik Persson, Anna Wedestig (2004)

Banach Center Publications

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B. Florkiewicz, A. Rybarski (1972)

Colloquium Mathematicae

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Stathis Filippas, Achilles Tertikas, Jesper Tidblom (2009)

Journal of the European Mathematical Society

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Mostafa A. Nasr (1977)

Annales Polonici Mathematici

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Hajer Bahouri, Jean-Yves Chemin, Isabelle Gallagher (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The aim of this article is to present “refined” Hardy-type inequalities. Those inequalities are generalisations of the usual Hardy inequalities, their additional feature being that they are invariant under oscillations: when applied to highly oscillatory functions, both sides of the refined inequality are of the same order of magnitude. The proof relies on paradifferential calculus and Besov spaces. It is also adapted to the case of the Heisenberg group.

Wu, Changhong, Liu, Lanzhe (2006)

Lobachevskii Journal of Mathematics

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R.N. Mohapatra, D.C. Russel (1985)

Aequationes mathematicae

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