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Littlewood-Paley g-functions with rough kernels on homogeneous groups

Yong Ding; Xinfeng Wu — 2009

Studia Mathematica

Let 𝔾 be a homogeneousgroup on ℝⁿ whose multiplication and inverse operations are polynomial maps. In 1999, T. Tao proved that the singular integral operator with Llog⁺L function kernel on ≫ is both of type (p,p) and of weak type (1,1). In this paper, the same results are proved for the Littlewood-Paley g-functions on 𝔾

Vector-valued inequalities for the commutators of fractional integrals with rough kernels

Yanping Chen; Xinfeng Wu; Honghai Liu — 2014

Studia Mathematica

Some conditions implying vector-valued inequalities for the commutator of a fractional integral and a fractional maximal operator are established. The results obtained are substantial improvements and extensions of some known results.

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