
An exact expression for the down norm is given in terms of the level function on all rearrangement invariant spaces and a useful approximate expression is given for the down norm on all rearrangement invariant spaces whose upper Boyd index is not one.
down norm, Banach spaces of continuous, differentiable or analytic functions, level function, Inequalities for sums, series and integrals, duality, Banach function space, rearrangement invariant space, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
down norm, Banach spaces of continuous, differentiable or analytic functions, level function, Inequalities for sums, series and integrals, duality, Banach function space, rearrangement invariant space, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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