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On a supremum operator. (English) Zbl 1260.26020

Brown, B. Malcolm (ed.) et al., Spectral theory, function spaces and inequalities. New techniques and recent trends. Dedicated to David Edmund and Des Evans to their 80th and 70th birthdays. Berlin: Springer (ISBN 978-3-0348-0262-8/hbk; 978-3-0348-0263-5/ebook). Operator Theory: Advances and Applications 219, 233-242 (2012).
Summary: For a supremum operator \(R_\varphi (t) := \text{esssup}_{y\in [t, \infty)}\Phi (y, t)\varphi (y)\) on the semi-axis with a measurable non-negative function \(\Phi (x, y)\) the weighted \(L_p -L_q\) boundedness on the cone of non-increasing functions is characterized.
For the entire collection see [Zbl 1227.00040].

MSC:

26D10 Inequalities involving derivatives and differential and integral operators
26D15 Inequalities for sums, series and integrals
26D07 Inequalities involving other types of functions
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