Vector and norm spaces
Lebesgue sequence and function spaces: Lebesgue sequence spaces and related theorems. Hardy and Hilbert inequalities. Essentialy bounded functions, Lebesgue spaces (p>1), Embeddings, Approximation in Lebesgue spaces, Duality, Reflexivity, weak convergence and continuity of translation operator, weighted Lebesgue spaces, Isometries, Lebesgue spaces (0<p<1).
Distribution Function and Rearangements: Distribution functions, Decreasing Rearangements, Rearanagement of Fourier Transform.
Weak Lebesgue spaces: Weak Lebesgue spaces, Convergence in Measure, Interpolation and Normability.
Lorentz Spaces: Lorentz space and Normability, Completeness, Separbility, Duality, Lorentz sequence spaces.
Non-Standard Function spaces: Variable Lebesgue space Definition and their properties. Some differences between constant exponent and variable exponent spaces. Grand Lebesgue space, Amalgam and Herz type spaces with variable exponents.
An Introductory Course in Lebesgue Spaces
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Optimization in Vector Spaces
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