MULTIVARIATE POLYNOMIAL INEQUALITIES OF DIFFERENT L-p, W (V)-METRICS WITH k-CONCAVE WEIGHTS

作者：Ganzburg M I^*

来源：Acta Mathematica Hungarica, 2016, 150(1): 99-120.

DOI：10.1007/s10474-016-0632-z

• multivariate polynomial
• polynomial inequality of different metrics
• (1/d)-concave measure
• log-concave measure

Let W be a k-concave weight on an open convex set V in , , and let be the weighted measure on V generated by W with . We find lower and upper estimates of a constant A in the inequality () where P is a polynomial of m variables of degree at most n. In the case of log-concave measures (k = 0) we improve estimates of A obtained by A. Brudnyi. For estimates of A are new, and we show that they are sharp with respect to n as . The proofs are based on distributional inequalities for polynomials obtained by Nazarov, Sodin, Volberg, and Fradelizi. Two new examples for a generalized Jacobi weight on [-1, 1] and a multivariate Gegenbauer-type weight on a convex body are included.

• 出版日期2016-10