Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Deshmukh, Aniruddha, Kumar, Ashisha
Institution: Indian Institute of Technology Indore
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Ministry of Education, India
OpenAlex ID: W7220693834