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Refining the Hölder and Minkowski inequalities.

Sinnamon, G. — 2001

Journal of Inequalities and Applications [electronic only]

Mapping properties of integral averaging operators

H. Heinig; G. Sinnamon — 1998

Studia Mathematica

Characterizations are obtained for those pairs of weight functions u and v for which the operators $T f (x) = ʃ_{a (x)}^{b (x)} f (t) d t$ with a and b certain non-negative functions are bounded from $L_{u}^{p} (0, \infty)$ to $L_{v}^{q} (0, \infty)$ , 0 < p,q < ∞, p≥ 1. Sufficient conditions are given for T to be bounded on the cones of monotone functions. The results are applied to give a weighted inequality comparing differences and derivatives as well as a weight characterization for the Steklov operator.

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