Sharp L^p-L^q estimates for generalized k-plane transforms

2007/01/04 by Philip T. Gressman, Gressman, Philip T.
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.math/0701114

openalex publication_date 2007/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, optimal L^p-L^q estimates are obtained for operators which average functions over polynomial submanifolds, generalizing the k-plane transform. An important advance over previous work is that full L^p-L^q estimates are obtained by methods which have traditionally yielded only restricted weak-type estimates. In the process, one is lead to make coercivity estimates for certain functionals on L^p for p < 1.

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