Algebras of Convolution Type Operators on Weighted Variable Lebesgue Spaces

• Autor(a) principal: Medalha, Samuel João Baltazar
• Data de Publicação: 2021
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10362/135865
• topic: Weighted variable Lebesgue spaces; Fourier multipliers; Interpolation; Functions of bounded variation; Slowly oscillating functions; Algebras of convolution type operators; Domínio/Área Científica::Ciências Naturais::Matemáticas

We prove a version of the Riesz-Thorin interpolation theorem for some types of weighted variable Lebesgue spaces. In order to do this we use the theory developed by Calderón in his 1964 article, together with some Banach function space theory. Using our version of the Riesz-Thorin theorem, we prove a version of the Stechkin inequality forweighted variable Lebesgue spaces, allowing us to define algebras of Fourier multipliers arising from functions of bounded variation. After analyzing the invertibility of Fourier convolution operators with piecewise continuous symbols, we shift our attention to slowly oscillating Fourier multipliers, finishing with a proof that the image in the Calkin algebra of the algebra of convolution type operators with slowly oscillating data is commutative.