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Fractional deformed Laplace operator and applications
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DOI：10.1080/00036811.2025.2611028.png)
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Abstract
En 中文
In this article, we introduce the generalized Riesz potentials associated to the deformed Hankel transform, we investigate their $ L<^>p $ Lp- $ L<^>q $ Lq boundedness properties. We define and we study the fractional deformed Laplace operator. In particular, we prove a Caffarelli-Silvestre type relation for the proposed fractional operator through an extension problem. Next, we derive some results for the fractional deformed Laplace operator via the Mellin transform.
Keywords:
Deformed Hankel transform
generalized translation
generalized convolution
generalized Riesz potential
generalized fractional maximal operator
fractional deformed Laplace operator
Mellin transform