Multiple singular integrals and maximal operators related to homogeneous mappings

Journal of Inequalities and Applications

Daiqing Zhang¹  Feng Liu²  Jing Zhang³ 

[1] College of Mathematics and Physics, Fujian University of Technology;College of Mathematics and Systems Science, Shandong University of Science and Technology;School of Mathematics and Statistics, Yili Normal College;

关键词: multiple singular integrals;    rough kernels;    maximal operators;    homogeneous mappings;   

DOI  :  10.1186/s13660-016-1164-3

来源: DOAJ

【 摘 要 】

Abstract In this paper, we present the L p $L^{p}$ mapping properties of multiple singular integrals related to homogeneous mappings with rough kernels given by the radial function h ∈ Δ γ $h\in\Delta_{\gamma}$ (or h ∈ U γ $h\in U_{\gamma}$ ) for some γ > 1 $\gamma>1$ (or γ ≥ 1 $\gamma\geq1$ ) and the sphere function Ω ∈ L ( log + L ) 2 ( S m − 1 × S n − 1 ) $\Omega\in L(\log^{+}L)^{2} (S^{m-1}\times S^{n-1})$ (or Ω ∈ L ( log + L ) 2 / γ ′ ( S m − 1 × S n − 1 ) $\Omega\in L(\log^{+}L)^{2/\gamma'} (S^{m-1}\times S^{n-1})$ ). In addition, the L p $L^{p}$ bounds for the related maximal operators are also given. Our main results extend and improve some known ones.

【 授权许可】

Unknown