Algebras of convolution type operators with continuous data do not always contain all rank one operators

DOI10.1007/s00020-021-02631-xzbMath1477.47095arXiv2007.10266OpenAlexW3151815090MaRDI QIDQ829809

Eugene Shargorodsky, Alexei Yu. Karlovich

Publication date: 6 May 2021

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.10266

zbMATH Keywords

Lorentz spaceHardy-Littlewood maximal operatorrank one operatoralgebra of convolution type operatorscontinuous Fourier multiplierseparable Banach function space

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Integral operators (47G10) Multipliers in one variable harmonic analysis (42A45) Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) (47L80)

Related Items (3)

On the weak convergence of shift operators to zero on rearrangement-invariant spaces ⋮ Invertibility of Fourier convolution operators with \textit{pc} symbols on variable Lebesgue spaces with Khvedelidze weights ⋮ Unnamed Item

Cites Work

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• Non-commutative Gelfand theories. A tool-kit for operator theorists and numerical analysts
• Boundedness and compactness of pseudodifferential operators with non-regular symbols on weighted Lebesgue spaces
• Functional analysis, Sobolev spaces and partial differential equations
• The dual of weak \(L^p\)
• Carleson curves, Muckenhoupt weights, and Toeplitz operators
• Algebras of convolution type operators with piecewise slowly oscillating data. I: Local and structural study
• Algebras of convolution type operators with piecewise slowly oscillating data. II: Local spectra and Fredholmness
• Calkin images of Fourier convolution operators with slowly oscillating symbols
• Algebras of continuous Fourier multipliers on variable Lebesgue spaces
• Semi-almost periodic Fourier multipliers on rearrangement-invariant spaces with suitable Muckenhoupt weights
• Noncompactness of Fourier convolution operators on Banach function spaces
• Banach algebra of the Fourier multipliers on weighted Banach function spaces
• Atomic decomposition of Hardy spaces and characterization of \(BMO\) via Banach function spaces
• \(C^*\)-algebras of integral operators with piecewise slowly oscillating coefficients and shifts acting freely
• Commutators of convolution type operators on some Banach function spaces
• Maximally Modulated Singular Integral Operators and their Applications to Pseudodifferential Operators on Banach Function Spaces
• On Convolution Type Operators with Piecewise Slowly Oscillating Data
• Classical Fourier Analysis
• Measure, Integration & Real Analysis
• Algebra of convolution type operators with continuous data on Banach function spaces
• The Cauchy Singular Integral Operator on Weighted Variable Lebesgue Spaces
• When does the norm of a Fourier multiplier dominate its L∞ norm?
• Function Spaces

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