On the Strict Majorant Property in Arbitrary Dimensions

In this work we study d-dimensional majorant properties. We prove that a set of frequencies in ℤ satisfies the strict majorant property on Lp([0,1]d) for all p > 0 if and only if the set is affinely independent. We further construct three types of violations of the strict majorant property. Any set of at least d + 2 frequencies in ℤ violates the strict majorant property on Lp([0,1]d) for an open interval of p∉2ℕ of length 2. Any infinite set of frequencies in ℤ violates the strict majorant property on Lp([0,1]d) for an infinite sequence of open intervals of p∉2ℕ of length 2. Finally, given any p > 0 with p∉2ℕ, we exhibit a set of d + 2 frequencies on the moment curve in ℝ that violate the strict majorant property on Lp([0,1]d).