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Convergence in L p-norm of Fourier series on the complete product of quaternion groups with bounded orders

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Abstract

A well-known result for Vilenkin systems is the fact that for all 1 < p < ∞ the n-th partial sums of Fourier series of all functions in the space L p converge to the function in L p-norm. This statement can not be generalized to any representative product system on the complete product of finite non-abelian groups, but even then it is true for the complete product of quaternion groups with bounded orders and monomial representative product system ordered in a specific way.

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Authors and Affiliations

  1. College of Nyíregyháza, Inst. of Math. and Comp. Sci., Nyíregyháza, P. O. Box 166, H-4400, Hungary

    György Gát & Rodolfo Toledo

Authors
  1. György Gát
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  2. Rodolfo Toledo
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Correspondence to György Gát.

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Supported by project TÁMOP-4.2.2.A-11/1/KONV-2012-00

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Gát, G., Toledo, R. Convergence in L p-norm of Fourier series on the complete product of quaternion groups with bounded orders. Acta. Math. Sin.-English Ser. 30, 1566–1578 (2014). https://doi.org/10.1007/s10114-014-3360-8

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  • DOI: https://doi.org/10.1007/s10114-014-3360-8

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