Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Extrapolation for multilinear compact operators and applications
HTML articles powered by AMS MathViewer

by Mingming Cao, Andrea Olivo and Kôzô Yabuta PDF
Trans. Amer. Math. Soc. 375 (2022), 5011-5070 Request permission


This paper is devoted to studying the Rubio de Francia extrapolation for multilinear compact operators. It allows one to extrapolate the compactness of $T$ from just one space to the full range of weighted spaces, whenever an $m$-linear operator $T$ is bounded on weighted Lebesgue spaces. This result is indeed established in terms of the multilinear Muckenhoupt weights $A_{\vec {p}, \vec {r}}$, and the limited range of the $L^p$ scale. To show extrapolation theorems above, by means of a new weighted Fréchet-Kolmogorov theorem, we present the weighted interpolation for multilinear compact operators. To prove the latter, we also need to build a weighted interpolation theorem in mixed-norm Lebesgue spaces. As applications, we obtain the weighted compactness of commutators of many multilinear operators, including multilinear $\omega$-Calderón-Zygmund operators, multilinear Fourier multipliers, bilinear rough singular integrals and bilinear Bochner-Riesz means. Beyond that, we establish the weighted compactness of higher order Calderón commutators, and commutators of Riesz transforms related to Schrödinger operators.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2020): 42B25, 42B20, 42B35
  • Retrieve articles in all journals with MSC (2020): 42B25, 42B20, 42B35
Additional Information
  • Mingming Cao
  • Affiliation: Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas, C/ Nicolás Cabrera, 13-15, E-28049 Madrid, Spain
  • MR Author ID: 1136109
  • Email:
  • Andrea Olivo
  • Affiliation: ICTP-The Abdus Salam International Centre for Theoretical Physics, Strada Costiera, 11, I-34151, Trieste, Italy
  • MR Author ID: 1361110
  • Email:
  • Kôzô Yabuta
  • Affiliation: Research Center for Mathematics and Data Science, Kwansei Gakuin University, Gakuen 2-1, Sanda 669-1337, Japan
  • ORCID: 0000-0002-9144-6491
  • Email:
  • Received by editor(s): March 7, 2021
  • Received by editor(s) in revised form: December 29, 2021
  • Published electronically: April 26, 2022
  • Additional Notes: The first author was supported by Spanish Ministry of Science and Innovation through the Juan de la Cierva-Formación 2018 (FJC2018-038526-I), through the “Severo Ochoa Programme for Centres of Excellence in R&D” (CEX2019-000904-S), and through PID2019-107914GB-I00, and by the Spanish National Research Council through the “Ayuda extraordinaria a Centros de Excelencia Severo Ochoa” (20205CEX001).
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 5011-5070
  • MSC (2020): Primary 42B25, 42B20, 42B35
  • DOI:
  • MathSciNet review: 4439498