### Abstract

The inequality (Formula presented) is proved for two-parameter trigonometric-Fourier coefficients and for the two-dimensional classical Hardy space H_{p} on the bidisc. The inequality (*) is extended to each p if the Fourier coefficients are monotone. For monotone coefficients and for every p, the supremum of the partial sums of the Fourier series is in L_{p} whenever the left hand side of (*) is finite. From this it follows that under the same condition the two-dimensional trigonometric-Fourier series of an arbitrary function from H_{1} converges a.e. and also in L_{1} norm to that function.

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

Pages (from-to) | 175-184 |

Number of pages | 10 |

Journal | Studia Mathematica |

Volume | 118 |

Issue number | 2 |

Publication status | Published - 1996 |

### Fingerprint

### Keywords

- Atomic decomposition
- Hardy spaces
- Hardy-Littlewood inequalities
- Rectangle p-atom

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Two-parameter Hardy-Littlewood inequalities.** / Weisz, F.

Research output: Contribution to journal › Article

*Studia Mathematica*, vol. 118, no. 2, pp. 175-184.

}

TY - JOUR

T1 - Two-parameter Hardy-Littlewood inequalities

AU - Weisz, F.

PY - 1996

Y1 - 1996

N2 - The inequality (Formula presented) is proved for two-parameter trigonometric-Fourier coefficients and for the two-dimensional classical Hardy space Hp on the bidisc. The inequality (*) is extended to each p if the Fourier coefficients are monotone. For monotone coefficients and for every p, the supremum of the partial sums of the Fourier series is in Lp whenever the left hand side of (*) is finite. From this it follows that under the same condition the two-dimensional trigonometric-Fourier series of an arbitrary function from H1 converges a.e. and also in L1 norm to that function.

AB - The inequality (Formula presented) is proved for two-parameter trigonometric-Fourier coefficients and for the two-dimensional classical Hardy space Hp on the bidisc. The inequality (*) is extended to each p if the Fourier coefficients are monotone. For monotone coefficients and for every p, the supremum of the partial sums of the Fourier series is in Lp whenever the left hand side of (*) is finite. From this it follows that under the same condition the two-dimensional trigonometric-Fourier series of an arbitrary function from H1 converges a.e. and also in L1 norm to that function.

KW - Atomic decomposition

KW - Hardy spaces

KW - Hardy-Littlewood inequalities

KW - Rectangle p-atom

UR - http://www.scopus.com/inward/record.url?scp=0002017406&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002017406&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0002017406

VL - 118

SP - 175

EP - 184

JO - Studia Mathematica

JF - Studia Mathematica

SN - 0039-3223

IS - 2

ER -