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

2017/08/24 by Shuichi Sato, Shūichi Satō, Sato, Shuichi
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Mathematical Analysis and Transform Methods #math.CA #msc:42B25 #msc:46E35

paper · pdf · doi:10.48550/arxiv.1708.07343

21 pages

arxiv created 2017/08/24 · arxiv updated 2017/08/25

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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