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Generalized Convolution Inequalities and Application

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Abstract

In this paper, we characterize \(L^p-L^q\) inequality involving a generalized convolution. The convolution that we use covers the standard convolution as well as many more. A reverse convolution inequality has also been discussed. We give an application of our inequalities, in particular, to find solution of heat equation in a wider class of solutions.

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Acknowledgements

The first author acknowledges with thanks CSIR, India for the research support (Ref. No. 25(0242)/15/EMR-II).

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Authors and Affiliations

  1. Department of Mathematics, South Asian University, Chanakya Puri, New Delhi, 110021, India

    Pankaj Jain

  2. Department of Mathematics, Vivekananda College (University of Delhi), Vivek Vihar, Delhi, 110095, India

    Sandhya Jain

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  1. Pankaj Jain
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  2. Sandhya Jain
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Correspondence to Pankaj Jain.

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Jain, P., Jain, S. Generalized Convolution Inequalities and Application. Mediterr. J. Math. 14, 159 (2017). https://doi.org/10.1007/s00009-017-0961-3

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  • DOI: https://doi.org/10.1007/s00009-017-0961-3

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