List questions from lp-spaces

Published on 06 Dec 2023 - 20:55

46

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Brezis' exercise 8.28.2: prove that $T$ is a compact operator

Published on 28 Mar 2026 - 14:55

109

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Brezis' exercise 8.28.4: how to prove that $\langle Tf, f \rangle \ge 0$?

Published on 06 Dec 2023 - 23:18

154

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A measure space which satisfying $\inf\{\mu(E): E\in M \text{ such that } \mu(E)>0\}=0$

Published on 08 Dec 2023 - 12:23

77

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Differentiability of convolution without compact support

Published on 08 Apr 2026 - 17:26

92

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Brezis' exercise 8.28.11: how to prove $\sum_{k=0}^{\infty} \left | \frac{1}{2} \alpha_k (f) - a \right |^2 < + \infty$?

Published on 07 Apr 2026 - 23:18

13

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Show $v(x,t) \in L^2([0,T];H^2(\mathbb{R}))$ when $v(x,t)$ is a transformation of a $L^2([0,T];H^2(\mathbb{R}))$ function

Published on 26 Mar 2026 - 8:00

221

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About the constant from the Marcinkiewicz Interpolation Theorem

Published on 09 Apr 2026 - 10:26

57

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If Fourier transform of a simple function $f$ satisfies inequality $\| \hat{f} \|_q \leq C\|f\|_p$ then $1/p + 1/q = 1$

Published on 08 Apr 2026 - 22:40

47

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Why is $L^2_0$ a complete subspace?

Published on 13 Dec 2023 - 15:56

32

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Proof of unitairity of regular representation

Published on 10 Apr 2026 - 14:35

80

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What is the name of this function space?

Published on 14 Dec 2023 - 8:24

63

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If $u(.,t) \in H^2(\mathbb{R})$, then $u (.,t) \in C^1(\mathbb{R})$?

Published on 28 Mar 2026 - 8:49

58

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Why almost sure convergence cannot imply convergence in $L^p$?

Published on 11 Apr 2026 - 20:34

141

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Show that no arbitrage implies the extension property in $L^p$

Published on 25 Mar 2026 - 22:03

List Question

Weak convergence argue

Brezis' exercise 8.28.2: prove that $T$ is a compact operator

Brezis' exercise 8.28.4: how to prove that $\langle Tf, f \rangle \ge 0$?

A measure space which satisfying $\inf\{\mu(E): E\in M \text{ such that } \mu(E)>0\}=0$

Differentiability of convolution without compact support

Brezis' exercise 8.28.11: how to prove $\sum_{k=0}^{\infty} \left | \frac{1}{2} \alpha_k (f) - a \right |^2 < + \infty$?

Show $v(x,t) \in L^2([0,T];H^2(\mathbb{R}))$ when $v(x,t)$ is a transformation of a $L^2([0,T];H^2(\mathbb{R}))$ function

About the constant from the Marcinkiewicz Interpolation Theorem

If Fourier transform of a simple function $f$ satisfies inequality $\| \hat{f} \|_q \leq C\|f\|_p$ then $1/p + 1/q = 1$

Why is $L^2_0$ a complete subspace?

Proof of unitairity of regular representation

What is the name of this function space?

If $u(.,t) \in H^2(\mathbb{R})$, then $u (.,t) \in C^1(\mathbb{R})$?

Why almost sure convergence cannot imply convergence in $L^p$?

Show that no arbitrage implies the extension property in $L^p$

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