### Abstract

It is shown that the maximal operator of the Marcinkiewicz means of a tempered distribution is bounded from H_{p}(R^{2}) to L_{p}(R^{2}) for all p_{0}

01(R^{2}) converge a.e. to the function in question. Moreover, we prove that the Marcinkiewicz means are uniformly bounded on the spaces H_{p}(R^{2}) and so they converge in the norm (p_{0}

Original language | English |
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Pages (from-to) | 675-695 |

Number of pages | 21 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 252 |

Issue number | 2 |

Publication status | Published - Dec 15 2000 |

### Fingerprint

### Keywords

- Atomic decomposition
- Hardy spaces
- Interpolation
- Marcinkiewicz means
- p-atom

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

**A generalization for Fourier transforms of a theorem due to Marcinkiewicz.** / Weisz, F.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 252, no. 2, pp. 675-695.

}

TY - JOUR

T1 - A generalization for Fourier transforms of a theorem due to Marcinkiewicz

AU - Weisz, F.

PY - 2000/12/15

Y1 - 2000/12/15

N2 - It is shown that the maximal operator of the Marcinkiewicz means of a tempered distribution is bounded from Hp(R2) to Lp(R2) for all p001(R2) converge a.e. to the function in question. Moreover, we prove that the Marcinkiewicz means are uniformly bounded on the spaces Hp(R2) and so they converge in the norm (p0

AB - It is shown that the maximal operator of the Marcinkiewicz means of a tempered distribution is bounded from Hp(R2) to Lp(R2) for all p001(R2) converge a.e. to the function in question. Moreover, we prove that the Marcinkiewicz means are uniformly bounded on the spaces Hp(R2) and so they converge in the norm (p0

KW - Atomic decomposition

KW - Hardy spaces

KW - Interpolation

KW - Marcinkiewicz means

KW - p-atom

UR - http://www.scopus.com/inward/record.url?scp=0034670551&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034670551&partnerID=8YFLogxK

M3 - Article

VL - 252

SP - 675

EP - 695

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -