Schur's lemma and best constants in weighted norm inequalities
AbstractStrong forms of Schur's Lemma and its converse are proved for maps taking non-negative functions to non-negative functions and having formal adjoints. These results are applied to give best constants in a large class of weighted Lebesgue norm inequalities for non-negative integral operators. Since general measures are used, norms of non-negative matrix operators may be calculated by the same method.
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