## Abstract

In this article, we establish a new atomic decomposition for f ε L ^{2} _{w} ∩ H ^{p} _{w} , where the decomposition converges in L ^{2} _{w}-norm rather than in the distribution sense. As applications of this decomposition, assuming that T is a linear operator bounded on L ^{2} _{w} and 0 < p ≤ 1, we obtain (i) if T is uniformly bounded in L ^{p} _{w} -norm for all w-p-atoms, then T can be extended to be bounded from HL ^{p} _{w} to L ^{p} _{w} ; (ii) if T is uniformly bounded in H ^{p} _{w} -norm for all w-p-atoms, then T can be extended to be bounded on H ^{p} _{w} ; (iii) if T is bounded on H ^{p} _{w} , then T can be extended to be bounded from H ^{p} _{w} to L ^{p} _{w}.

Original language | English |
---|---|

Pages (from-to) | 303-314 |

Number of pages | 12 |

Journal | Canadian Mathematical Bulletin |

Volume | 55 |

Issue number | 2 |

DOIs | |

State | Published - 2012 |

## Keywords

- A weights
- Atomic decomposition
- Calderón reproducing formula
- Weighted hardy spaces