List questions from hardy-spaces

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Rudin RCA Chapter 17 Exercise 3

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Blaschke product: What does extending continuously mean here?

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Functions in $A(\mathbb{C})$ that vanish at zero

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Hardy operator and its adjoint

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Checking that a function is in Hardy-2 space of the unit disc around the origin

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Major error in classic "Banach Spaces of Analytic Functions"

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Every simple functions in $L_p(\mathbb{T}) $ is a trigonometric polynomial.

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restrictions of analytic functions to the circle

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Functional proof of nonexistence of an integral pairing

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Vanishing of one-half of Fourier coefficients implies boundary of $H^p$-space function

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Riesz representation theorem for functionals acting on Hölder $C^\alpha$ functions

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Orthogonal complement of $BH^2$, where B is Blaschke

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Find a weighted Sobolev space $X\subset L^1(\mathbb R^n)$ such that, if $u\in X$ and has zero mean, then $u$ is in the Hardy space $\mathcal H^1$.

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Example of a function which is in Hardy space $H^1(\mathbb{D})$ but not in $H^2(\mathbb{D})$

Published on 04 Oct 2023 - 9:58

List Question

Blaschke product having poles proof

Rudin RCA Chapter 17 Exercise 3

Blaschke product: What does extending continuously mean here?

Functions in $A(\mathbb{C})$ that vanish at zero

Hardy operator and its adjoint

Checking that a function is in Hardy-2 space of the unit disc around the origin

Major error in classic "Banach Spaces of Analytic Functions"

Every simple functions in $L_p(\mathbb{T}) $ is a trigonometric polynomial.

restrictions of analytic functions to the circle

Functional proof of nonexistence of an integral pairing

Vanishing of one-half of Fourier coefficients implies boundary of $H^p$-space function

Riesz representation theorem for functionals acting on Hölder $C^\alpha$ functions

Orthogonal complement of $BH^2$, where B is Blaschke

Find a weighted Sobolev space $X\subset L^1(\mathbb R^n)$ such that, if $u\in X$ and has zero mean, then $u$ is in the Hardy space $\mathcal H^1$.

Example of a function which is in Hardy space $H^1(\mathbb{D})$ but not in $H^2(\mathbb{D})$

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