Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

On a conjecture of F. Móricz

Author(s): G. Brown; K. Y. Wang
Journal: Proc. Amer. Math. Soc. 126 (1998), 3527-3537.
MSC (1991): Primary 42B05
MathSciNet review: 1452795
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Abstract | References | Similar articles | Additional information

Abstract: F. Móricz has investigated the integrability of double lacunary sine series. His result, valid for special lacunary sequences, does not extend in the form originally conjectured, but we establish a suitably modified result.

References:

1.: C.-P. Chen, Integrability of multiple trigonometric series and parseval's formula, J. Math. Anal. Appl. 186 (1994), 182-199. MR 95h:42011
2.: -, Weighted integrability and -convergence of multiple trigonometric series, Studia Math. 108 (1994), 177-190. MR 95b:42010
3.: F. Móricz, Integrability of double lacunary sine series, Proc. of the AMS 110 (1990), 355-364. MR 90m:42020
4.: L. V. Zhizhiashvili, Certain questions from the theory of simple and multiple trigonometric and orthogonal series, Uspekhi Mat. Nauk 28 (1973), 65-127.

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Additional Information:

G. Brown
Affiliation: Vice-Chancellor, University of Sydney, Sydney, New South Wales 2006, Australia
Email: m.jackson@vcc.usyd.edu.au

K. Y. Wang
Affiliation: Department of Mathematics, Beijing Normal University, 100871 Beijing, People's Republic of China
Email: wangky@email.bnu.edu.cn

DOI: 10.1090/S0002-9939-98-04375-5
PII: S 0002-9939(98)04375-5
Keywords: Double sine series, lacunarity, integrability
Received by editor(s): June 22, 1993
Received by editor(s) in revised form: February 12, 1997
Additional Notes: This work was supported by a grant from the Australian Research Council.
Communicated by: J. Marshall Ash
Copyright of article: Copyright 1998, American Mathematical Society

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