2026-06-29T02:09:58Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/1304692026-01-16T13:17:45Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Carro Rossell, María Jesús
2026-01-16T13:17:45Z
2026-01-16T13:17:45Z
2025-14
Carro, M. J. Analytic Families of Operators in Extrapolation Theory with Application to Average Operators. In The Mathematical Heritage of Guido Weiss (pp. 127-143). Cham: Springer Nature Switzerland. 2025 Jan 31: 127-143
https://hdl.handle.net/20.500.14352/130469
Our goal is to prove weak type boundedness for an operator which is given as an average of a family of operators satisfying certain estimates in the context of weighted Lebesgue spaces.
Our main technique is inspired on the theory of analytic families of operators and it is closely related to the Rubio de Francia’s extrapolation theory.
eng
Analytic families of operators in extrapolation theory with application to average operators
book part
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