PreprintCC BY 4.0arXiv
On the mapping properties of a radially power-weighted k-plane transform
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 Lp-improving boundedness and end-point Lorentz space estimates. Finally, we look at the weighted Lp-Lp boundedness of the operator acting on general functions, and evaluate its operator norm.
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BibTeX
@misc{deshmukh2026mapping,
title = {{On the mapping properties of a radially power-weighted k-plane transform}},
author = {Aniruddha Deshmukh and Ashisha Kumar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04503},
eprint = {2610.04503},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04503},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the mapping properties of a radially power-weighted k-plane transform
AU - Aniruddha Deshmukh
AU - Ashisha Kumar
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04503
UR - https://arxiv.org/abs/2610.04503
AB - 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.
ER -