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تسجيل مستخدم جديدReverse Triangle Inequalities for Riesz Potentials and Connections with Polarization
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We study reverse triangle inequalities for Riesz potentials and their connection with polarization. This work generalizes inequalities for sup norms of products of polynomials, and reverse triangle inequalities for logarithmic potentials. The main tool used in the proofs is the representation for a power of the farthest distance function as a Riesz potential of a unit Borel measure.
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We study the reverse triangle inequalities for suprema of logarithmic potentials on compact sets of the plane. This research is motivated by the inequalities for products of supremum norms of polynomials. We find sharp additive constants in the inequ
alities for potentials, and give applications of our results to the generalized polynomials. We also obtain sharp inequalities for products of norms of the weighted polynomials $w^nP_n, deg(P_n)le n,$ and for sums of suprema of potentials with external fields. An important part of our work in the weighted case is a Riesz decomposition for the weighted farthest-point distance function.
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Let ${mathcal P}_k$ denote the set of all algebraic polynomials of degree at most $k$ with real coefficients. Let ${mathcal P}_{n,k}$ be the set of all algebraic polynomials of degree at most $n+k$ having exactly $n+1$ zeros at $0$. Let $$|f|_A := su
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