### Abstract

The two-dimensional classical Hardy spaces H_{p}(T×T) on the bidisc are introduced and it is shown that the maximal operator of the Cesàro means of a distribution is bounded from H_{p}(T×T) to L_{p}(T^{2}) (3/4

#_{1}(T×T), L_{1}(T^{2})) where the Hardy space H^{#}_{1}(T×T) is defined by the hybrid maximal function. As a consequence we obtain that the Cesàro means of a function f∈H^{#}_{1}(T×T) ⊃L log L(T^{2}) converge a.e. to the function in question.

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

Pages (from-to) | 30-45 |

Number of pages | 16 |

Journal | Journal of Approximation Theory |

Volume | 90 |

Issue number | 1 |

Publication status | Published - Jul 1997 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Analysis
- Applied Mathematics
- Numerical Analysis

### Cite this

*Journal of Approximation Theory*,

*90*(1), 30-45.

**Cesàro summability of two-parameter trigonometric-Fourier series.** / Weisz, F.

Research output: Contribution to journal › Article

*Journal of Approximation Theory*, vol. 90, no. 1, pp. 30-45.

}

TY - JOUR

T1 - Cesàro summability of two-parameter trigonometric-Fourier series

AU - Weisz, F.

PY - 1997/7

Y1 - 1997/7

N2 - The two-dimensional classical Hardy spaces Hp(T×T) on the bidisc are introduced and it is shown that the maximal operator of the Cesàro means of a distribution is bounded from Hp(T×T) to Lp(T2) (3/4#1(T×T), L1(T2)) where the Hardy space H#1(T×T) is defined by the hybrid maximal function. As a consequence we obtain that the Cesàro means of a function f∈H#1(T×T) ⊃L log L(T2) converge a.e. to the function in question.

AB - The two-dimensional classical Hardy spaces Hp(T×T) on the bidisc are introduced and it is shown that the maximal operator of the Cesàro means of a distribution is bounded from Hp(T×T) to Lp(T2) (3/4#1(T×T), L1(T2)) where the Hardy space H#1(T×T) is defined by the hybrid maximal function. As a consequence we obtain that the Cesàro means of a function f∈H#1(T×T) ⊃L log L(T2) converge a.e. to the function in question.

UR - http://www.scopus.com/inward/record.url?scp=0031185072&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031185072&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031185072

VL - 90

SP - 30

EP - 45

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

SN - 0021-9045

IS - 1

ER -