Parabolic Littlewood-Paley g-function with rough kernel

In this note, we give the L^p （1 〈 p 〈∞） boundedness of the parabolic Littlewood Paley g-function with rough kernel.     

带Hardy空间函数核的Marcinkiewicz积分的L~p有界性

本文证明了一类分别相应于 Ｌｉｔｔｌｅｗｏｏｄ－Ｐａｌｅｇ ｇ函数, 函数和面积积分Ｓ的 Ｍａｒｃｉｎｋｉｅｗｉｃｚ积分算子,μΩ,μ~*Ω,λ和μΩ,ｓ的 Ｌ~p（Ｒ~n）有界性．其中核函数Ω∈Ｈ~１（Ｓ（ｎ－１））这里Ｈ~１（Ｓ（ｎ－１））记Ｒ~ｎ（ｎ ≤２）中的单位球面 Ｈａｒｄｒ空间．本文结果是已知结果的本质改进和推广．     

Heisenberg群上Lilltewood-Paley算子的有界性

得到了Heisenberg群上的广义Littlewood-Paley算子g＊ψ,λ从H^˙Kq^α,p （Hn）空间到^˙Kq^α,p （Hn）空间的有界性,其中Q（1-1/q）≤α〈Q（1-1/q）＋1.当α=Q（1-1/q）＋1时,得到算子g^＊ψ,λ从H^˙Kq^α,p （Hn）空间到W^˙Kq^α,p （Hn）空间的有界性.     

参数型Littlewood-Paley算子在带非双倍测度Morrey空间上的有界性

假定μ是仅满足一个增长条件的Radon测度,即存在一个正常数C 使得对所有的 x∈R^d , r 〉0以及对某个固定的n∈（0,d]都成立μ（B（x,r））≤Cr^n.对适当的参数ρ和λ,证明了参数型gλ^＊函数Mλ^＊ρ和参数型Marcinkiewicz积分M^ρ在Morrey空间M q^p （k,μ）上是有界的.     

Regularity Criteria for the Navier-Stokes Equations Containing Two Velocity Components

Based on the critical sobolev inequalities in the Besov spaces with the logarithmic form, the regularity criteria in terms of two velocity components for the 3D incompressible Navier-Stokes equations are improved.     

The Boundedness of Littlewood-Paley Operators with Rough Kernels on Weighted $(L^q,L^p)^{\alpha}(\mathbf{R}^n)$ Spaces

In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral $\mu_{\Omega,s}$ and Littlewood-Paley functions $\mu_{\Omega}$ and $\mu^{*}_{\lambda}$ on the weighted amalgam spaces $(L^{q}_\omega,L^{p})^{\alpha}(\mathbf{R}^{n})$ as $1 < q\leq \alpha < p\leq \infty$.     

Littlewood-Paley operators with variable kernels

In this paper we study a certain directional Hilbert transform and the bound-edness on some mixed norm spaces. As one of applications, we prove the Lp-boundedness of the Littlewood-Paley operators with variable kernels. Our results are extensions of some known theorems.