Article
Lorentz spaces of vector measures and real interpolation of operators
Author/s | Campo Acosta, Ricardo del
Fernández Carrión, Antonio Mayoral Masa, Fernando Naranjo Naranjo, Francisco José Sánchez Pérez, Enrique A. |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Publication Date | 2020 |
Deposit Date | 2022-07-28 |
Published in |
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Abstract | Using the representation of the real interpolation of spaces of p-integrable
functions with respect to a vector measure, we show new factorization theorems for p th power factorable operators acting in interpolation couples ... Using the representation of the real interpolation of spaces of p-integrable functions with respect to a vector measure, we show new factorization theorems for p th power factorable operators acting in interpolation couples of Banach function spaces. The recently introduced Lorentz spaces of the semivariation of vector mea sures play a central role in the resulting factorization theorems. We apply our results to analyze extension of operators from classical weighted Lebesgue L p -spaces — in general with different weights — that can be extended to their q-th powers. This is the case, for example, of the convolution operators defined by L p -improving mea-sures acting in Lebesgue L p -spaces or Lorentz spaces. A new representation theorem for Banach lattices with a special lattice geometric property, as a space of vector measure integrable functions, is also proved. |
Funding agencies | Ministerio de Economía y Competitividad (MINECO). España |
Project ID. | MTM2016-77054-C2-1-P2 |
Citation | Campo Acosta, R.d., Fernández Carrión, A., Mayoral Masa, F., Naranjo Naranjo, F.J. y Sánchez Pérez, E.A. (2020). Lorentz spaces of vector measures and real interpolation of operators. Quaestiones Mathematicae, 43 (5-6), 591-609. |
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