Introduction to Functional Analysis, R. Meise and D. Vogt. Despite the name, that's nowhere near just an introduction, especially Part III. Classical and Mult

Introduction to Functional Analysis, R. Meise and D. Vogt. Despite the name, that's nowhere near just an introduction, especially Part III. Classical and Multilinear Harmonic Analysis, C. Muscalu and W. Schlag. After reading the two volumes you will have a huge base of knowledge. The books can get quite advanced as well, containing previously unpublished results when being first printed.