Lorentz spaces of vector measures and real interpolation of operators. Issue 5 (3rd August 2020)

• Record Type: Journal Article
• Authors: del Campo, R.; Fernández, A.; Mayoral, F.; Naranjo, F.; Sánchez Pérez, E.A.
• Is Part Of: Quaestiones mathematicae. Volume 43:Issue 5/6(2020)
• Page Start: 591
• Page End: 609
• Publication Date: 2020-08-03
• Subjects: Primary 46E30 -- Secondary 47B38, 46B42; Banach function space -- vector measure -- real interpolation -- factorable operator -- bidual concave operator -- improving measures; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2019.1605413
• Languages: English
• ISSNs: 1607-3606

Abstract

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 of Banach function spaces. The recently introduced Lorentz spaces of the semivariation of vector measures 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 measures 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.