Abstract
The aim of this paper is to prove an \(\mathcal {L}_q^1 \cap \mathcal {L}_q^2\) versions of Nash and Carlson’s inequalities for a class of q-integral operator \(\mathcal {T}_q\) with a bounded kernel. As applications, we give q-analogues of Nash and Carlson’s inequalities for the q-Fourier-cosine, q-Fourier-sine, q-Dunkl and q-Bessel Fourier transforms.
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Communicated by Laurent Baratchart.
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Hleili, M., Brahim, K. On Nash and Carlson’s Inequalities for Symmetric q-Integral Transforms. Complex Anal. Oper. Theory 10, 1339–1350 (2016). https://doi.org/10.1007/s11785-015-0523-2
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DOI: https://doi.org/10.1007/s11785-015-0523-2