Weak type estimates for functions of Marcinkiewicz type with fractional integrals of mixed homogeneity

Key Points

• The aim is to establish endpoint weak type estimates for square functions of Marcinkiewicz type involving fractional integrals with mixed homogeneity.
• Proved weak type estimates for square functions under non-isotropic dilations.
• Considered fractional integrals of mixed homogeneity instead of traditional Riesz potentials.
• Applied theoretical frameworks to generalize C. Fefferman's result.
• Established endpoint weak type estimates for the discussed functions.
• Generalized existing results related to Marcinkiewicz type functions.
• Showed implications for the analysis of fractional integrals in non-isotropic contexts.