The sharp range of L p -estimates for the class of Hörmander-type oscillatory integral operators is established in all dimensions under a positivedefinite assumption on the phase. This is achieved by generalising a recent approach of the first author for studying the Fourier extension operator, which utilises polynomial partitioning arguments. The main result implies improved bounds for the Bochner-Riesz conjecture in dimensions n ě 4.3 Strictly speaking, in [9] weaker L 8´Lp bounds are proven, but the methods can be used to establish the L p´Lp strengthening: see, for instance, [14, §9] where the L p´Lp argument appears (although in a slightly disguised form). 4 In particular, Lee [19] proved that for positive-definite phases (1.4) holds for p ě 2¨n`2 n in all dimensions, extending the range in Theorem 1.1 when n is odd.

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Abstract. We identify complete monotonicity properties underlying a variety of well-known sharp Strichartz inequalities in euclidean space.

Let 𝔏 be a collection of L lines in ℝ3 and J the set of joints formed by 𝔏, that is, the set of points each of which lies in at least three non‐coplanar lines of 𝔏. It is known that |J| ≲ L3/2 (first proved by Guth and Katz). For each joint x∈J, let the multiplicity N(x) of x be the number of triples of non‐coplanar lines through x. We prove here that ∑x∈JN(x)1/2 ≲ L3/2, while in the last section we extend this result to real algebraic curves of bounded degree in ℝ3, as well as to curves in ℝ3 parametrized by polynomials of bounded degree.