English

Rank and regularity for averages over submanifolds

Classical Analysis and ODEs 2008-02-05 v1

Abstract

This paper establishes endpoint LpLqL^p-L^q and Sobolev mapping properties of Radon-like operators which satisfy a homogeneity condition (similar to semiquasihomogeneity) and a condition on the rank of a matrix related to rotational curvature. For highly degenerate operators, the rank condition is generically satisfied for algebraic reasons, similar to an observation of Greenleaf, Pramanik, and Tang concerning oscillatory integral operators.

Keywords

Cite

@article{arxiv.0802.0428,
  title  = {Rank and regularity for averages over submanifolds},
  author = {Philip T. Gressman},
  journal= {arXiv preprint arXiv:0802.0428},
  year   = {2008}
}

Comments

32 pages, 2 figures

R2 v1 2026-06-21T10:09:20.892Z