Weak and strong boundedness for p-adic fractional Hausdorff operator and its commutator

In this paper, the boundedness of the Hausdorff operator on weak central Morrey space is obtained. Furthermore, we investigate the weak bounds of the p-adic fractional Hausdorff operator on weighted p-adic weak Lebesgue spaces. We also obtain the sufficient condition of commutators of the p-adic fractional Hausdorff operator by taking symbol function from Lipschitz spaces. Moreover, strong type estimates for fractional Hausdorff operator and its commutator on weighted p-adic Lorentz spaces are also acquired.

Morrey Meets Herz with Variable Exponent and Applications to Commutators of Homogeneous Fractional Integrals with Rough Kernels

We define the new central Morrey space with variable exponent and investigate its relation to the Morrey-Herz spaces with variable exponent. As applications, we obtain the boundedness of the homogeneous fractional integral operator TΩ,σ and its commutator [b,TΩ,σ] on Morrey-Herz space with variable exponent, where Ω∈Ls(Sn-1) for s≥1 is a homogeneous function of degree zero, 0<σ<n, and b is a BMO function.

Some Estimates of Rough Bilinear Fractional Integral

We study the boundedness of rough bilinear fractional integralBΩ,αon Morrey spacesLp,λ(ℝn)and modified Morrey spacesL~p,λ(ℝn)and obtain some sufficient and necessary conditions on the parameters. Furthermore, we consider the boundedness ofBΩ,αon generalized central Morrey spaceB˙p,φ(ℝn). These extend some known results.