Demonstrates weak type estimates for square functions of Marcinkiewicz type, suggesting a generalization of known results.
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.
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Sato et al. (2019) studied this question.
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