Title: Maximal Function Methods for Sobolev Spaces
Subjects: Mathematics, Sobolev spaces, Maximal functions, Inequalities (Mathematics), Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theory, Functional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of "smooth'' functions, embedding theorems, trace theorems, Real functions -- Inequalities -- Inequalities involving derivatives and differential and integral operators, Measure and integration -- Classical measure theory -- Contents, measures, outer measures, capacities, Potential theory -- Higher-dimensional theory -- Potentials and capacities, extremal length and related notions in higher dimensions, Partial differential equations -- General topics in partial differential equations -- Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals, Partial differential equations -- Elliptic equations and systems -- Quasilinear elliptic equations with $p$-Laplacian, Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Harmonic analysis and PDE