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On the Sobolev boundedness results of the product of pseudo-differential operators involving a couple of fractional Hankel transforms

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Abstract

This article is concerned with the study of pseudo-differential operators associated with fractional Hankel transform. The product of two fractional pseudo-differential operators is defined and investigated its basic properties on some function space. It is shown that the pseudo-differential operators and their products are bounded in Sobolev type spaces. Particular cases are discussed.

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Acknowledgements

The authors would like to express their gratitude to the referees for their valuable suggestion and comments to improve the manuscript and to write the final form of this article.

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Authors and Affiliations

  1. Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, India

    Akhilesh Prasad

  2. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Kanailal Mahato

Authors
  1. Akhilesh Prasad
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  2. Kanailal Mahato
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Corresponding author

Correspondence to Kanailal Mahato.

Additional information

The first author is supported by CSIR, New Delhi (Grant No. 25 (240)/15/EMR-II)

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Prasad, A., Mahato, K. On the Sobolev boundedness results of the product of pseudo-differential operators involving a couple of fractional Hankel transforms. Acta. Math. Sin.-English Ser. 34, 221–232 (2018). https://doi.org/10.1007/s10114-017-7151-x

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  • DOI: https://doi.org/10.1007/s10114-017-7151-x

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