Concept

Hardy space

Related lectures (31)

Delves into the completeness of Lp spaces and the density of function classes in L².

Introduces Lp spaces, covering norms, inequalities, and integrability of functions.

Martingale Convergence Theorem: Proof and Recap

Covers the proof and recap of the martingale convergence theorem, focusing on the conditions for the existence of a random variable.

Analysis IV: Le Spaces

Introduces Le spaces, measurable functions, Holder inequality, and LP space properties.

Barycenter and Young Measures

Explains barycenter, weak convergence, uniqueness of limits, distances, and Young measures in LP spaces.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Interior Regularity Results

Explores interior regularity results, focusing on weak solutions and unique selection in mathematical analysis.

Distributions & Interpolation Spaces

Explores convolution operators, interpolation spaces, and function convergence in different spaces.

Lecture 4: Hilbert Spaces and Unique Solutions

Covers Hilbert spaces and unique solutions in function spaces, emphasizing the Lax-Milgram theorem.

Advanced Mathematical Analysis

Covers advanced topics in mathematical analysis, including cubes, electrical operators, LP spaces, and compact operators.

Measure Spaces: Integration and Inequalities

Covers measure spaces, integration, Radon-Nikodym property, and inequalities like Jensen, Hölder, and Minkowski.

Linear Statics of Deformable Solids

Introduces linear statics for linear elastic solids in small deformations, stress equilibrium, the Virtual Work Principle, and the Finite Element Method.

Examples: Function Spaces

Covers various examples of function spaces and linear applications between them.

Embedding in Function Spaces

Explores embedding in function spaces, including elliptic equations, Hölder inequality, Lorentz space, and Hardy-Young inequality.

Norm Equivalence and Inverse Inequality

Explores norm equivalence, inverse inequality, and error analysis in finite element methods.

Continuity and Galerkin Method

Introduces continuity in function spaces and the Galerkin method for solving boundary value problems.

Martingale Convergence Theorem

Explains the martingale convergence theorem and its applications in probability theory.

Measure Spaces: O-Finite and Probability Measures

Explores o-finite and finite measure spaces, probability measures, and inequalities, concluding with LP space completeness.

Distribution to Spaces: Interpolation and Continuity

Covers weak derivatives, interpolation spaces, and continuity in function spaces.

Scalar Products: Definition, Examples

Covers the definition of a scalar product on a real vector space and provides examples.