Interpolation of 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.

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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.

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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

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Boundedness for Multilinear Singular Integral Operators on Some Hardy and Herz Type Spaces

Georgian Mathematical Journal ◽

10.1515/gmj.2005.309 ◽

2005 ◽

Vol 12 (2) ◽

pp. 309-320

Author(s):

Lanzhe Liu

Keyword(s):

Singular Integral ◽

Integral Operators ◽

Singular Integral Operators ◽

Lipschitz Functions ◽

Multilinear Operators ◽

Multilinear Singular Integral ◽

Type Spaces

Abstract In this paper, we prove the boundedness for some multilinear operators generated by singular integral operators and Lipschitz functions on some Hardy and Herz type spaces.

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