• Symmetric polynomials and lp inequalities for certain intervals of p, Vol 37, No.1

Authors: Klemes, Ivo, Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec, H3A 2K6, Canada (klemes@math.mcgill.ca).
Symmetric polynomials and lp inequalities for certain intervals of p, pp. 285-295.
ABSTRACT. We prove some sufficient conditions implying lp inequalities of the form ||x||p ≤ ||y||p for vectors x, y in Rn and for p in certain positive real intervals. Our sufficient conditions are strictly weaker than the usual majorization relation. The conditions are expressed in terms of certain homogeneous symmetric polynomials in the entries of the vectors. These polynomials include the elementary symmetric polynomials as a special case. We also give a characterization of the majorization relation by means of symmetric polynomials.

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Symmetric polynomials and lp inequalities for certain intervals of p, Vol 37, No.1

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