The measure of noncompactness of multilinear operators. (November 2019)

• Record Type: Journal Article
• Authors: Kokilashvili, Vakhtang; Mastyło, Mieczysław; Meskhi, Alexander
• Is Part Of: Nonlinear analysis. Volume 188(2019)
• Page Start: 70
• Page End: 79
• Publication Date: 2019-11
• Subjects: primary 46B70 42B30; Multilinear operators -- Mutilinear Hilbert and Riesz transform -- Measure of noncompactness -- Compact operators -- Approximation property; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.05.011
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We investigate the multilinear variants of the quantities which measure the noncompactness of multilinear operators taking values in Banach spaces with the uniform approximation property. We show applications to multilinear variant of the Hilbert and Riesz transform on rearrangement invariant spaces. We derive lower estimates of the essential norm of these transforms. Along the way we obtain also as a by-product the lower estimates of the measure noncompactness of these transforms. As a consequence we conclude that the Hilbert and Riesz transforms are not compact multilinear transforms.