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Fourier analysis with respect to bilinear maps

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Abstract

Several results about convolution and about Fourier coefficients for X-valued functions defined on the torus satisfying the condition sup‖y‖=1 ∫ π−π ‖ B(f(eiϑ), y)‖dϑ/2π < ∞ for a bounded bilinear map B: X × Y → Z are presented and some applications are given.

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Authors and Affiliations

  1. Department of Mathematics, Universitat de València, Burjassot, 46100, Valencia, Spain

    O. Blasco

  2. Department of Applied Mathematics, Universidad Politécnica de Valencia, 46022, Valencia, Spain

    J. M. Calabuig

Authors
  1. O. Blasco
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  2. J. M. Calabuig
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Corresponding author

Correspondence to O. Blasco.

Additional information

The authors gratefully acknowledges support by Spanish Grants MTM2005-08350-C03-03 and MTN2004-21420 -E. J.M. Calabuig is also supported by Generalitat Valenciana (Project GV/2007/191)

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Blasco, O., Calabuig, J.M. Fourier analysis with respect to bilinear maps. Acta. Math. Sin.-English Ser. 25, 519–530 (2009). https://doi.org/10.1007/s10114-009-7399-x

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  • DOI: https://doi.org/10.1007/s10114-009-7399-x

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