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arXiv · 2610.04503

On the mapping properties of a radially power-weighted k-plane transform

Aniruddha Deshmukh·Ashisha Kumar
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Abstract

In this article, we study a weighted analogue of the $k$-plane transform, where the weight on the $k$-dimensional measure is given by a radial power of distance. Particularly, we first consider the existence of such operators on Lebesgue spaces imbibed with radial power weights. Then, we proceed to see the mapping properties of the said transform when it acts on radial functions. In this regard, we prove certain weighted $L^p$-improving boundedness and end-point Lorentz space estimates. Finally, we look at the weighted $L^p$-$L^p$ boundedness of the operator acting on general functions, and evaluate its operator norm.

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Aniruddha Deshmukh, Ashisha Kumar. 2026-10-03. On the mapping properties of a radially power-weighted k-plane transform. https://arxiv.org/abs/2610.04503

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