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

Shuichi Sato

Studia Mathematica (1996)

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

Abstract

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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.

How to cite

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Sato, 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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  1. [1] S. Bochner, Summation of multiple Fourier series by spherical means, Trans. Amer. Math. Soc. 40 (1936), 175-207. Zbl62.0293.03
  2. [2] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Clarendon Press, Oxford, 1954. Zbl0058.03301
  3. [3] T. W. Körner, Everywhere divergent Fourier series, Colloq. Math. 45 (1981), 103-118. Zbl0491.42011
  4. [4] S. Sato, Spherical summability and a vector-valued inequality, Bull. London Math. Soc. 27 (1995), 58-64. Zbl0821.42011
  5. [5] S. Sato, A weighted vector-valued weak type (1, 1) inequality and spherical summation, Studia Math. 109 (1994), 159-170. Zbl0826.42010
  6. [6] S. Sato, Weak type estimates for some maximal operators on the weighted Hardy spaces, Ark. Mat., to appear. Zbl0852.47016
  7. [7] S. Sato, Some weighted weak type estimates for rough operators, preprint, March 1995. 
  8. [8] E. M. Stein, On limits of sequences of operators, Ann. of Math. 74 (1961), 140-170. Zbl0103.08903
  9. [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. [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. [11] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, N.J., 1971. Zbl0232.42007
  12. [12] J.-O. Strömberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in Math. 1381, 1989, Springer, Berlin. 
  13. [13] R. Wheeden, A boundary value characterization of weighted H 1 , Enseign. Math. 24 (1976), 121-134. Zbl0324.31003
  14. [14] A. Zygmund, Trigonometric Series, Cambridge Univ. Press, 1968. Zbl0157.38204

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