Extrapolation for bilinear compact operators in the variable exponent setting

2025/12/10 by Spyridon Kakaroumpas, Kakaroumpas, Spyridon, Stefanos Lappas +1
Mathematics · #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2512.09721

openalex publication_date 2025/12/10 · openalex created_date 2025/12/12 · openalex updated_date 2026/07/28

Abstract

We establish extrapolation of compactness for bilinear operators in the scale of weighted variable exponent Lebesgue spaces. First, we prove an abstract principle relying on the Cobos-Fernández-Cabrera-Martínez theorem. Then, as an application we deduce new compactness results for the commutators of bilinear ω-Calderón-Zygmund operators, bilinear fractional integrals and bilinear Fourier multipliers acting on weighted variable exponent Lebesgue spaces. Our work extends and unifies among others earlier works of the second named author together with Hytönen as well as Oikari.

Citations

• Factorizations for variable exponent Muckenhoupt weights
• Boundedness of a class of multilinear operators and their iterated commutators on Morrey-Banach function spaces
• A note on one sided extrapolation of compactness and applications
• A note on extrapolation of compactness
• Extrapolation on function and modular spaces, and applications
• Weighted norm inequalities for the bilinear maximal operator on variable Lebesgue spaces
• Extrapolation and weighted norm inequalities in the variable Lebesgue spaces
• Compactness properties of commutators of bilinear fractional integrals
• New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory
• Multilinear Calderón–Zygmund Theory

Related

• A note on extrapolation of compactness
• Compact bilinear commutators: the weighted case
• Extrapolation of compactness on weighted spaces II: Off-diagonal and limited range estimates
• Operators of Harmonic Analysis in Weighted Spaces with Non-standard Growth
• Kato-Ponce inequalities on weighted and variable Lebesgue spaces