Weak type estimates for functions of Marcinkiewicz type with fractional integrals of mixed homogeneity - Sato, Shuichi (MATHEMATICA SCANDINAVICA, 2019)
We prove the endpoint weak type estimate for square functions of Marcinkiewicz type with fractional integrals associated with non-isotropic dilations. This generalizes a result of C. Fefferman on functions of Marcinkiewicz type by considering fractional integrals of mixed homogeneity in place of the Riesz potentials of Euclidean structure.