### Abstract

The d-dimensional classical Hardy spaces H _{p}(T ^{d}) are introduced and it is shown that the maximal operator of the (C, α) (α = (α _{1},... , α _{d})) means of a distribution is bounded from H _{p}(T ^{d}) to L _{p}(T ^{d}) (d/(d + 1), 1/(α _{k} + 1) <p <∞) provided that the supremum in the maximal operator is taken over a positive cone. Moreover, we prove that the (C, α) means are uniformly bounded on the spaces H _{p}(T ^{d}) whenever d/(d+ 1), 1/(α _{k} + 1) <p <∞. Thus, in case f ∈ H _{p}(T), the Cesàro means converge to f in H _{p}(T ^{d}) norm (d/(d + 1), 1/(α _{k} + 1) <p <∞). The same results are proved for the conjugate (C, α) means, too.

Original language | English |
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Pages (from-to) | 705-720 |

Number of pages | 16 |

Journal | Publicationes Mathematicae |

Volume | 52 |

Issue number | 3-4 |

Publication status | Published - 1998 |

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### Keywords

- (C, α) summability
- Atomic decomposition
- Conjugate function
- Hardy spaces
- Interpolation
- p-atom

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Publicationes Mathematicae*,

*52*(3-4), 705-720.

**(C, α) means of d-dimensional trigonometric-Fourier series.** / Weisz, F.

Research output: Contribution to journal › Article

*Publicationes Mathematicae*, vol. 52, no. 3-4, pp. 705-720.

}

TY - JOUR

T1 - (C, α) means of d-dimensional trigonometric-Fourier series

AU - Weisz, F.

PY - 1998

Y1 - 1998

N2 - The d-dimensional classical Hardy spaces H p(T d) are introduced and it is shown that the maximal operator of the (C, α) (α = (α 1,... , α d)) means of a distribution is bounded from H p(T d) to L p(T d) (d/(d + 1), 1/(α k + 1) p(T d) whenever d/(d+ 1), 1/(α k + 1) p(T), the Cesàro means converge to f in H p(T d) norm (d/(d + 1), 1/(α k + 1)

AB - The d-dimensional classical Hardy spaces H p(T d) are introduced and it is shown that the maximal operator of the (C, α) (α = (α 1,... , α d)) means of a distribution is bounded from H p(T d) to L p(T d) (d/(d + 1), 1/(α k + 1) p(T d) whenever d/(d+ 1), 1/(α k + 1) p(T), the Cesàro means converge to f in H p(T d) norm (d/(d + 1), 1/(α k + 1)

KW - (C, α) summability

KW - Atomic decomposition

KW - Conjugate function

KW - Hardy spaces

KW - Interpolation

KW - p-atom

UR - http://www.scopus.com/inward/record.url?scp=0346367660&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346367660&partnerID=8YFLogxK

M3 - Article

VL - 52

SP - 705

EP - 720

JO - Publicationes Mathematicae

JF - Publicationes Mathematicae

SN - 0033-3883

IS - 3-4

ER -