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Weighted Hankel Transform and Its Applications to Fourier Transform

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Abstract

The purpose of the present paper is to discuss the integrability of the Fourier transform of \(L^\infty \)-functions subject to a very weak decay condition. This will include the negative power of the logarithm. For a start, the case when \(d=1\) is investigated by the use of the second mean value theorem. Based on the discussion of this case, a passage to the weighted Hankel transform is done, which covers the integrability of the d-dimensional Fourier transform of the radial functions.

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Acknowledgements

The authors are supported by Grant-in-Aid for Scientific Research (C), No. 19K03546, Japan Society for the Promotion of Science. The authors are thankful to anonymous referees for their kind comments which made the authors aware of many recent researches in this field.

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Correspondence to Yoshihiro Sawano.

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Communicated by Elijah Liflyand.

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Okada, M., Sawano, Y. Weighted Hankel Transform and Its Applications to Fourier Transform. J Fourier Anal Appl 27, 23 (2021). https://doi.org/10.1007/s00041-021-09831-4

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  • DOI: https://doi.org/10.1007/s00041-021-09831-4

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