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A class of commutators for multilinear fractional integrals in nonhomogeneous spaces.

Lian, Jiali; Wu, Huoxiong — 2008

Journal of Inequalities and Applications [electronic only]

Boundedness of higher order commutators of oscillatory singular integrals with rough kernels

Huoxiong Wu — 2005

Studia Mathematica

The author studies the commutators generated by a suitable function a(x) on ℝⁿ and the oscillatory singular integral with rough kernel Ω(x)|x|ⁿ and polynomial phase, where Ω is homogeneous of degree zero on ℝⁿ, and a(x) is a BMO function or a Lipschitz function. Some mapping properties of these higher order commutators on $L^{p} (ℝ ⁿ)$ , which are essential improvements of some well known results, are given.

A note on multilinear Muckenhoupt classes for multiple weights

Songqing Chen; Huoxiong Wu; Qingying Xue — 2014

Studia Mathematica

This paper is devoted to investigating the properties of multilinear $A_{P ⃗}$ conditions and $A_{(P ⃗, q)}$ conditions, which are suitable for the study of multilinear operators on Lebesgue spaces. Some monotonicity properties of $A_{P ⃗}$ and $A_{(P ⃗, q)}$ classes with respect to P⃗ and q are given, although these classes are not in general monotone with respect to the natural partial order. Equivalent characterizations of multilinear $A_{(P ⃗, q)}$ classes in terms of the linear $A_{p}$ classes are established. These results essentially improve and extend...

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Currently displaying 1 – 3 of 3

A class of commutators for multilinear fractional integrals in nonhomogeneous spaces.

Boundedness of higher order commutators of oscillatory singular integrals with rough kernels

A note on multilinear Muckenhoupt classes for multiple weights