Three--parameter weighted Hardy type inequalities.

Oinarov, R.; Kalybay, A.

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Some integral inequalities of Hardy type

B. Florkiewicz (1980)

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First and second order Opial inequalities

Steven Bloom (1997)

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Let $T_{γ} f (x) = ʃ_{0}^{x} k {(x, y)}^{γ} f (y) d y$ , where k is a nonnegative kernel increasing in x, decreasing in y, and satisfying a triangle inequality. An nth-order Opial inequality has the form $ʃ_{0}^{\infty} (\prod_{i = 1}^{n} | T_{γ_{i}} {f (x) |}^{q_{i}} {|) | f (x) |}^{q_{0}} w (x) d x \leq C (ʃ_{0}^{\infty} {| f (x) |}^{p} {v (x) d x)}^{(q_{0} + \dots + q_{n}) / p}$ . Such inequalities can always be simplified to nth-order reduced inequalities, where the exponent $q_{0} = 0$ . When n = 1, the reduced inequality is a standard weighted norm inequality, and characterizing the weights is easy. We also find necessary and sufficient conditions on the weights for second-order reduced Opial inequalities to hold. ...

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Brown, R.C. (2008)

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Josip E. Pečarić (1982)

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E. Sawyer (1985)

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Norm inequalities in weighted amalgam

Suket Kumar (2018)

Commentationes Mathematicae Universitatis Carolinae

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Hardy inequalities for the Hardy-type operators are characterized in the amalgam space which involves Banach function space and sequence space.

Hardy-Poincaré type inequalities derived from p-harmonic problems

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.