## Abstract

In this article, we use a discrete Calderón-type reproducing formula and Plancherel-Pôlya-type inequality associated to a para-accretive function to characterize the Triebel-Lizorkin spaces of para-accretive type F· ^{a,q} _{b,p} , which reduces to the classical Triebel-Lizorkin spaces when the para-accretive function is constant. Moreover, we give a necessary and sufficient condition for the F· ^{0,q} _{1,p} -F· ^{0,q} _{b,p} boundedness of paraproduct operators. From this, we show that a generalized singular integral operator T with MbTMb ε WBP is bounded from F· ^{0,q} _{1,p} to F· ^{0,q} _{b,p} if and only if T b ε F· ^{0,q} _{b,∞} and T *b = 0 for n/n+e <p = 1 and n/ n+e <q ≤ 2, where e is the regularity exponent of the kernel of T.

Original language | English |
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Pages (from-to) | 667-694 |

Number of pages | 28 |

Journal | Journal of Geometric Analysis |

Volume | 19 |

Issue number | 3 |

DOIs | |

State | Published - Jul 2009 |

## Keywords

- Calderón reproducing formula
- Para-accretive function
- Paraproduct operator
- Plancherel-Pôlya inequality
- T b theorem
- Triebel-Lizorkin space