# Divergence of the Bochner-Riesz means in the weighted Hardy spaces

Studia Mathematica (1996)

- Volume: 118, Issue: 3, page 261-275
- ISSN: 0039-3223

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topSato, Shuichi. "Divergence of the Bochner-Riesz means in the weighted Hardy spaces." Studia Mathematica 118.3 (1996): 261-275. <http://eudml.org/doc/216277>.

@article{Sato1996,

abstract = {We costruct functions in $H_\{w\}^\{1\}$ ($w ∈ A_\{1\}$) whose Fourier integral expansions are almost everywhere non-summable with respect to the Bochner-Riesz means of the critical order.},

author = {Sato, Shuichi},

journal = {Studia Mathematica},

keywords = {Bochner-Riesz means; weighted Hardy spaces; almost everywhere divergence; maximal operator},

language = {eng},

number = {3},

pages = {261-275},

title = {Divergence of the Bochner-Riesz means in the weighted Hardy spaces},

url = {http://eudml.org/doc/216277},

volume = {118},

year = {1996},

}

TY - JOUR

AU - Sato, Shuichi

TI - Divergence of the Bochner-Riesz means in the weighted Hardy spaces

JO - Studia Mathematica

PY - 1996

VL - 118

IS - 3

SP - 261

EP - 275

AB - We costruct functions in $H_{w}^{1}$ ($w ∈ A_{1}$) whose Fourier integral expansions are almost everywhere non-summable with respect to the Bochner-Riesz means of the critical order.

LA - eng

KW - Bochner-Riesz means; weighted Hardy spaces; almost everywhere divergence; maximal operator

UR - http://eudml.org/doc/216277

ER -

## References

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- [6] S. Sato, Weak type estimates for some maximal operators on the weighted Hardy spaces, Ark. Mat., to appear. Zbl0852.47016
- [7] S. Sato, Some weighted weak type estimates for rough operators, preprint, March 1995.
- [8] E. M. Stein, On limits of sequences of operators, Ann. of Math. 74 (1961), 140-170. Zbl0103.08903
- [9] E. M. Stein, An ${H}^{1}$ function with non-summable Fourier expansions, in: Lecture Notes in Math. 992, Springer, Berlin, 1983, 193-200.
- [10] E. M. Stein, M. H. Taibleson and G. Weiss, Weak type estimates for maximal operators on certain ${H}^{p}$ classes, Rend. Circ. Mat. Palermo (2), Suppl. 1 (1981), 81-97. Zbl0503.42018
- [11] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, N.J., 1971. Zbl0232.42007
- [12] J.-O. Strömberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in Math. 1381, 1989, Springer, Berlin.
- [13] R. Wheeden, A boundary value characterization of weighted ${H}^{1}$, Enseign. Math. 24 (1976), 121-134. Zbl0324.31003
- [14] A. Zygmund, Trigonometric Series, Cambridge Univ. Press, 1968. Zbl0157.38204

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