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Weighted inequalities for monotone functions.

L. Maligranda — 1997

Collectanea Mathematica

We give characterizations of weights for which reverse inequalities of the Hölder type for monotone functions are satisfied. Our inequalities with general weights and with sharp constants complement previous results.

Inequalities and interpolation.

L. MaligrandaL. E. Persson — 1993

Collectanea Mathematica

Some examples of the close interaction between inequalities and interpolation are presented and discussed. An interpolation technique to prove generalized Clarkson inequalities is pointed out. We also discuss and apply to the theory of interpolation the recently found facts that the Gustavsson-Peetre class P can be described by one Carlson type inequality and that the wider class P can be characterized by another Carlson type inequality with blocks.

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