Integral Equations and Operator Theory

, Volume 76, Issue 1, pp 55–79

Singular Integrals on Product Homogeneous Groups

Article

DOI: 10.1007/s00020-013-2049-1

Cite this article as:
Ding, Y. & Sato, S. Integr. Equ. Oper. Theory (2013) 76: 55. doi:10.1007/s00020-013-2049-1

Abstract

We consider singular integral operators with rough kernels on the product space of homogeneous groups. We prove Lp boundedness of them for \({p \in (1,\infty)}\) under a sharp integrability condition of the kernels.

Mathematics Subject Classification (2010)

Primary 42B20 

Keywords

multiple singular integrals homogeneous groups 

Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Laboratory of Mathematics and Complex Systems (BNU), Ministry of Education, School of Mathematical SciencesBeijing Normal UniversityBeijingPeople’s Republic of China
  2. 2.Department of Mathematics, Faculty of EducationKanazawa UniversityKanazawaJapan