MAXIMAL SEMIGROUP SYMMETRY AND DISCRETE RIESZ TRANSFORMS
MAXIMAL SEMIGROUP SYMMETRY AND DISCRETE RIESZ TRANSFORMS
We raise a question of whether the Riesz transform on $\mathbb{T}^{n}$ or $\mathbb{Z}^{n}$ is characterized by the ‘maximal semigroup symmetry’ that the transform satisfies. We prove that this is the case if and only if the dimension is one, two or a multiple of four. This generalizes a theorem of …