Linear functional equations and their solutions in Lorentz spaces

DOI10.1007/s13398-022-01259-9OpenAlexW3119380492MaRDI QIDQ2144422

Thomas Zürcher, Janusz Morawiec

Publication date: 13 June 2022

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.02428

zbMATH Keywords

functional equationslinear operatorsLorentz spacesapproximate differentiabilityLuzin's condition \(N\)

Mathematics Subject Classification ID

Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Linear operators on function spaces (general) (47B38) Iteration theory, iterative and composite equations (39B12) Equations and inequalities involving linear operators, with vector unknowns (47A50)

Cites Work

• One-dimensional functional equations
• On functions with derivatives in a Lorentz space
• Advanced analysis on the real line
• Linear functional equations and their solutions in generalized Orlicz spaces
• Some classes of linear operators involved in functional equations
• Some new functional spaces
• On totally differentiable and smooth functions
• Every Convex Function is Locally Lipschitz
• Fine behavior of functions whose gradients are in an Orlicz space
• Change of variables formula under minimal assumptions
• Sobolev Spaces on Metric Measure Spaces
• Convex functions and their applications. A contemporary approach
• Recent results on functional equations in a single variable, perspectives and open problems
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