A permanence property for dominated multilinear operators

We study the boundedness of weighted multilinear operators given by products of finite vectors of Calderón-Zygmund operators. We also investigate weighted estimates for bilinear operators related to Schrödinger operator.

Download Full-text

Pietsch’s variants of s-numbers for multilinear operators

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas ◽

10.1007/s13398-021-01123-2 ◽

2021 ◽

Vol 115 (4) ◽

Author(s):

D. L. Fernandez ◽

M. Mastyło ◽

E. B. Silva

Keyword(s):

Linear Operator ◽

Linear Operators ◽

Multilinear Operators ◽

Dual Operator ◽

Range Space ◽

Linear Forms ◽

Fundamental Properties

AbstractWe study variants of s-numbers in the context of multilinear operators. The notion of an $$s^{(k)}$$ s ( k ) -scale of k-linear operators is defined. In particular, we shall deal with multilinear variants of the $$s^{(k)}$$ s ( k ) -scales of the approximation, Gelfand, Hilbert, Kolmogorov and Weyl numbers. We investigate whether the fundamental properties of important s-numbers of linear operators are inherited to the multilinear case. We prove relationships among some $$s^{(k)}$$ s ( k ) -numbers of k-linear operators with their corresponding classical Pietsch’s s-numbers of a generalized Banach dual operator, from the Banach dual of the range space to the space of k-linear forms, on the product of the domain spaces of a given k-linear operator.

Download Full-text

COARSE COHERENCE OF METRIC SPACES AND GROUPS AND ITS PERMANENCE PROPERTIES

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972718000977 ◽

2018 ◽

Vol 98 (3) ◽

pp. 422-433

Author(s):

BORIS GOLDFARB ◽

JONATHAN L. GROSSMAN

Keyword(s):

Metric Spaces ◽

General Context ◽

Metric Geometry ◽

Finitely Generated ◽

Coherence Property ◽

Finitely Generated Groups ◽

Permanence Property ◽

Permanence Properties ◽

New Framework

We introduce properties of metric spaces and, specifically, finitely generated groups with word metrics, which we call coarse coherence and coarse regular coherence. They are geometric counterparts of the classical algebraic notion of coherence and the regular coherence property of groups defined and studied by Waldhausen. The new properties can be defined in the general context of coarse metric geometry and are coarse invariants. In particular, they are quasi-isometry invariants of spaces and groups. The new framework allows us to prove structural results by developing permanence properties, including the particularly important fibering permanence property, for coarse regular coherence.

Download Full-text

Weighted estimates for vector-valued commutators of multilinear operators

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210504000976 ◽

2008 ◽

Vol 138 (04) ◽

pp. 897-921 ◽

Cited By ~ 18

Author(s):

Lin Tang

Keyword(s):

Multilinear Operators ◽

Weighted Estimates ◽

Vector Valued

Download Full-text