Fredholm criteria for Wiener-Hopf operators with continuous symbols acting on some Banach function spaces

2025/09/17 by Márcio Valente, Valente, Márcio · 1 citation
Mathematics · #Holomorphic and Operator Theory #Advanced Harmonic Analysis Research #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.2509.13996

Abstract

Let X(ℝ₊) be one of the following three Banach function spaces: a Lorentz space L^{p, q}(ℝ₊) with 1 < p, q < ∞; a reflexive Orlicz space L^Φ(ℝ₊); or a variable Lebesgue space L^p(⋅)(ℝ₊) with variable exponent p(⋅)∈ B_M(ℝ). We extend the Fredholm criteria for Wiener-Hopf operators with continuous symbols on the Lebesgue space L^p(ℝ₊), 1 < p < ∞, obtained by Roland Duduchava in the late 1970s, to the space X(ℝ₊).

Citations

• Calkin images of Fourier convolution operators with slowly oscillating symbols
• Algebras of convolution type operators with continuous data do not always contain all rank one operators
• Algebras of Continuous Fourier Multipliers on Variable Lebesgue Spaces
• Maximally Modulated Singular Integral Operators and their Applications to Pseudodifferential Operators on Banach Function Spaces

Cited by

• Lower estimates for the norm and the Kuratowski measure of moncompactness of Wiener-Hopf type operators

Related

• Pseudodifferential Operators on Variable Lebesgue Spaces
• Gohberg-Krupnik Localisation for Discrete Wiener-Hopf Operators on Orlicz Sequence Spaces
• Wiener-Hopf operators on spaces of functions on R+ with values in a Hilbert space
• A Wiener algebra for Fock space operators
• Maximal Noncompactness of Wiener-Hopf Operators