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

2017/08/24 by Shūichi Satō, Sato, Shuichi
Mathematics · #Advanced Harmonic Analysis Research #Mathematical Analysis and Transform Methods #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.1708.07343

Abstract

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.

Citations

• Parabolic maximal functions associated with a distribution, II

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