## Abstract

It is well-known that Calderón-Zygmund operators T are bounded on H ^{p} for n/n+1 < p ≤ 1 provided T*(1) = 0. In this article, it is shown that if T*(b) = 0, where b is a para-accretive function, T is bounded from the classical Hardy space H ^{p} to a new Hardy space H _{b} ^{p} . To develop an H _{b} ^{p} theory, a discrete Calderón-type reproducing formula and Plancherel-Pôlya- type inequalities associated to a para-accretive function are established. Moreover, David, Journé, and Semmes' result [9] about the L ^{P}, 1 < p < ∞, boundedness of the Littlewood-Paley g function associated to a para-accretive function is generalized to the case of p ≤ 1. A new characterization of the classical Hardy spaces by using more general cancellation adapted to para-accretive functions is also given. These results complement the celebrated Calderón-Zygmund operator theory.

Original language | English |
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Pages (from-to) | 291-318 |

Number of pages | 28 |

Journal | Journal of Geometric Analysis |

Volume | 14 |

Issue number | 2 |

DOIs | |

State | Published - 2004 |

## Keywords

- Calderón-Zygmund operator
- Hardy space
- Littlewood-Paley g function
- Plancherel-Plôya inequality
- Tb theorem
- discrete Calderón formula