On a conjecture of F. Móricz
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- by G. Brown and K. Y. Wang PDF
- Proc. Amer. Math. Soc. 126 (1998), 3527-3537 Request permission
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
- Chang P’ao Ch’ên, Integrability of multiple trigonometric series and Parseval’s formula, J. Math. Anal. Appl. 186 (1994), no. 1, 182–199. MR 1290651, DOI 10.1006/jmaa.1994.1293
- Chang P’ao Ch’ên, Weighted integrability and $L^1$-convergence of multiple trigonometric series, Studia Math. 108 (1994), no. 2, 177–190. MR 1259503, DOI 10.4064/sm-108-2-177-190
- Ferenc Móricz, Integrability of double lacunary sine series, Proc. Amer. Math. Soc. 110 (1990), no. 2, 355–364. MR 1021902, DOI 10.1090/S0002-9939-1990-1021902-5
- L. V. Zhizhiashvili, Certain questions from the theory of simple and multiple trigonometric and orthogonal series, Uspekhi Mat. Nauk 28 (1973), 65–127.
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
- 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 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 3527-3537
- MSC (1991): Primary 42B05
- DOI: https://doi.org/10.1090/S0002-9939-98-04375-5
- MathSciNet review: 1452795