BOUNDEDNESS OF GENERALIZED RIESZ POTENTIALS ON SPACES OF HOMOGENEOUS TYPE

作者：Liu, Liguang; Yang, Dachun^*; Zhou, Yuan

来源：Mathematical Inequalities & Applications, 2010, 13(4): 867-885.

DOI：10.7153/mia-13-63

• space of homogeneous type
• Hardy space
• atom
• molecule
• BMO
• Lipschitz space
• Riesz potential
• commutator

The authors introduce a class of generalized Riesz potentials with kernels having weak regularity on spaces of homogeneous type in the sense of Coifman and Weiss and establish their boundedness on Lebesgue spaces and Hardy spaces. As applications, the authors obtain the boundedness on Lebesgue spaces and Hardy spaces of commutators generated by Lipschitz functions and generalized Riesz potentials or Calderon-Zygmund operators with kernels having weak regularity on spaces of homogeneous type.

• 出版日期2010-10
• 单位北京师范大学