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

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Abstract

金沢大学人間社会研究域学校教育系

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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