Displaying similar documents to “The Choquet integral as Lebesgue integral and related inequalities”

Transferring monotonicity in weighted norm inequalities.

Gord Sinnamon (2003)

Collectanea Mathematica

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Certain weighted norm inequalities for integral operators with non-negative, monotone kernels are shown to remain valid when the weight is replaced by a monotone majorant or minorant of the original weight. A similar result holds for operators with quasi-concave kernels. To prove these results a careful investigation of the functional properties of the monotone envelopes of a non-negative function is carried-out. Applications are made to function space embeddings of the cones of monotone...