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Free, publicly-accessible full text available February 1, 2026
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We provide a simple criterion on a family of functions that implies a square function estimate on for every even integer . This defines a new type of superorthogonality that is verified by checking a less restrictive criterion than any other type of superorthogonality that is currently known.more » « less
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Abstract We prove almost everywhere convergence of continuous-time quadratic averages with respect to two commuting $$\mathbb {R}$$ -actions, coming from a single jointly measurable measure-preserving $$\mathbb {R}^2$$ -action on a probability space. The key ingredient of the proof comes from recent work on multilinear singular integrals; more specifically, from the study of a curved model for the triangular Hilbert transform.more » « less
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