On the square function associated with generalized Bochner-Riesz means

Original · EN

We consider generalized Bochner-Riesz multipliers of the form (1-ρ(ξ))+λ where ρ:R² belongs to a class of rough distance functions homogeneous with respect to a nonisotropic dilation group. We prove a critical L⁴ estimate for the associated square function, which we use to derive multiplier theorems for multipliers of the form m∘ρ where m:R.