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.
The behaviour of square functions from ergodic theory in $L^{\infty}$
Sparse domination and $L^{p} \rightarrow L^{q}$ estimates for maximal functions associated with curvature
Weak and strong $A_p$-$A_\infty$ estimates for square functions and related operators
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