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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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We interpret into decoupling language a refinement of a 1973 argument due to Karatsuba on Vinogradov's mean value theorem. The main goal of our argument is to answer what precisely solution counting in older partial progress on Vinogradov's mean value theorem corresponds to in Fourier decoupling theory.more » « less
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Abstract In this study, the solution of the Neumann problem associated with the CR Yamabe operator on a subset \Omegaof the CR manifold {{\mathbb{S}}}^{3}bounded by the Clifford torus \Sigmais discussed. The Yamabe-type problem of finding a contact form on \Omegawhich has zero Tanaka-Webster scalar curvature and for which \Sigmahas a constant p-mean curvature is also discussed.more » « less
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