Abstract
If \(\lambda > 0,v > 0,\lambda + v < 1\), and z is defined by \({z_n} = \sum\limits_{i + j = n} {{x_i}{y_j},{_r}(x) = {{\left( {\sum {x_i^r} } \right)}^{1/r}},}\) then
with equality only if all the x, or all the y, or all the x but one and all the y but one, are zero.
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Mitrinović, D.S., Pečarić, J.E., Fink, A.M. (1991). Convolution, Rearrangement and Related Inequalities. In: Inequalities Involving Functions and Their Integrals and Derivatives. Mathematics and Its Applications, vol 53. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3562-7_10
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