A quantitative version of Krein's theorem.

M. Fabian; P. Hájek; V. Montesinos; V. Zizler

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Multi-parameter paraproducts.

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We prove that classical Coifman-Meyer theorem holds on any polidisc T or arbitrary dimension d ≥ 1.

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The volume near the zeroes of a smooth function.

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A generalized sharp Whitney theorem for jets.

Charles Fefferman (2005)

Revista Matemática Iberoamericana

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Suppose that, for each point x in a given subset E ⊂ R, we are given an m-jet f(x) and a convex, symmetric set σ(x) of m-jets at x. We ask whether there exist a function F ∈ C(R) and a finite constant M, such that the m-jet of F at x belongs to f(x) + Mσ(x) for all x ∈ E. We give a necessary and sufficient condition for the existence of such F, M, provided each σ(x) satisfies a condition that we call "Whitnet w-convexity".