# A weighted vector-valued weak type (1,1) inequality and spherical summation

Studia Mathematica (1994)

- Volume: 109, Issue: 2, page 159-170
- ISSN: 0039-3223

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topSato, Shuichi. "A weighted vector-valued weak type (1,1) inequality and spherical summation." Studia Mathematica 109.2 (1994): 159-170. <http://eudml.org/doc/216066>.

@article{Sato1994,

abstract = {We prove a weighted vector-valued weak type (1,1) inequality for the Bochner-Riesz means of the critical order. In fact, we prove a slightly more general result.},

author = {Sato, Shuichi},

journal = {Studia Mathematica},

keywords = {vector-valued weak type (1,1) inequality; spherical summation; Bochner- Riesz operator; Fourier transform},

language = {eng},

number = {2},

pages = {159-170},

title = {A weighted vector-valued weak type (1,1) inequality and spherical summation},

url = {http://eudml.org/doc/216066},

volume = {109},

year = {1994},

}

TY - JOUR

AU - Sato, Shuichi

TI - A weighted vector-valued weak type (1,1) inequality and spherical summation

JO - Studia Mathematica

PY - 1994

VL - 109

IS - 2

SP - 159

EP - 170

AB - We prove a weighted vector-valued weak type (1,1) inequality for the Bochner-Riesz means of the critical order. In fact, we prove a slightly more general result.

LA - eng

KW - vector-valued weak type (1,1) inequality; spherical summation; Bochner- Riesz operator; Fourier transform

UR - http://eudml.org/doc/216066

ER -

## References

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- [2] M. Christ, Weak type endpoint bounds for Bochner-Riesz multipliers, Rev. Mat. Iberoamericana 3 (1987), 25-31. Zbl0726.42009
- [3] M. Christ and J. L. Rubio de Francia, Weak type (1,1) bounds for rough operators, II, Invent. Math. 93 (1988), 225-237. Zbl0695.47052
- [4] M. Christ and C. D. Sogge, The weak type ${L}^{1}$ convergence of eigenfunction expansions for pseudodifferential operators, ibid. 94 (1988), 421-453. Zbl0678.35096
- [5] S. Hofmann, Weighted weak-type (1,1) inequalities for rough operators, Proc. Amer. Math. Soc. 107 (1989), 423-435. Zbl0694.42024
- [6] M. Kaneko and G. Sunouchi, On the Littlewood-Paley and Marcinkiewicz functions in higher dimensions, Tôhoku Math. J. 37 (1985), 343-365. Zbl0579.42011
- [7] S. Z. Lu, M. Taibleson and G. Weiss, On the almost everywhere convergence of Bochner-Riesz means of multiple Fourier series, in: Lecture Notes in Math. 908, Springer, Berlin, 1982, 311-318.
- [8] S. Sato, Entropy and almost everywhere convergence of Fourier series, Tôhoku Math. J. 33 (1981), 593-597. Zbl0497.42005
- [9] S. Sato, Spherical summability and a vector-valued inequality, preprint, 1992.
- [10] A. Seeger, Endpoint estimates for multiplier transformations on compact manifolds, Indiana Univ. Math. J. 40 (1991), 471-533. Zbl0737.42012
- [11] X. Shi and Q. Sun, preprint, Hangzhou University, Hangzhou, 1991.
- [12] F. Soria and G. Weiss, Indiana Univ. Math. J., to appear.
- [13] E. M. Stein, An ${H}^{1}$ function with non-summable Fourier expansion, in: Lecture Notes in Math. 992, Springer, Berlin, 1983, 193-200.
- [14] J.-O. Strömberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in Math. 1381, Springer, Berlin, 1989.
- [15] A. Vargas, Ph.D. thesis, Universidad Autónoma de Madrid.
- [16] A. Zygmund, Trigonometric Series, Cambridge Univ. Press, 1968. Zbl0157.38204

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