Stability of Localized Integral Operators on Weighted L^p spaces

2011/07/09 by Kyung Soo Rim, Rim, Kyung Soo, Chang Eon Shin +3 · 1 citation
Mathematics · #31B10 #42C99 #44A35 #45P05 #46E30 #47B38 #47G10 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory (math.SP) #math.FA #math.SP #msc:31B10 #msc:42C99 #msc:44A35 #msc:45P05 #msc:46E30 #msc:47B38 #msc:47G10

paper · pdf · doi:10.48550/arxiv.1107.1818

arxiv created 2011/07/09 · openalex publication_date 2011/07/09 · arxiv updated 2011/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider localized integral operators whose kernels have mild singularity near the diagonal and certain Holder regularity and decay off the diagonal. Our model example is the Bessel potential operator \mathcal J_γ, γ>0. We show that if such a localized integral operator has stability on a weighted function space L^p_w for some p∈ [1, ∞) and Muckenhoupt A_p-weight w, then it has stability on weighted function spaces L^p'_w' for all 1≤ p'<∞ and Muckenhoupt A_p'-weights w'.

Cited by

• Inverse-closedness of weighted Schur and BGS type quasi-Banach algebras

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