Question

Minimizing an integral -- Hilbert space

score 1.1k · Answer 1 · 2026-04-12 21:51:09

1.1k

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Minimizing an integral -- Hilbert space

Published on 12 Apr 2026 - 21:51

score 73 · Answer 2 · 2026-04-14 19:35:40

73

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Is it true that $\lim\limits_{r \rightarrow 1}f(r x) = f(x)$ in $L^1$?

Published on 14 Apr 2026 - 19:35

score 164 · Answer 3 · 2026-04-14 19:31:38

164

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Spaces of functions similar to $L^p$ but with different local and global sizes

Published on 14 Apr 2026 - 19:31

score 4.9k · Answer 4 · 2026-04-13 05:09:07

4.9k

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Intuitive explanation of $L^2$-norm

Published on 13 Apr 2026 - 5:09

score 203 · Answer 5 · 2026-04-13 19:15:06

203

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Is it natural how $L^p$ spaces measure local and global sizes the same?

Published on 13 Apr 2026 - 19:15

score 69 · Answer 6 · 2026-04-15 05:22:09

69

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Subspace of $L^1(\Omega)$ closed

Published on 15 Apr 2026 - 5:22

score 648 · Answer 7 · 2026-04-11 10:33:41

648

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Properties of sequences of bounded functions in $L^2$

Published on 11 Apr 2026 - 10:33

score 80 · Answer 8 · 2026-03-28 01:26:19

80

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If $\{\nabla u_j\}$ is Cauchy in $L^p(\mathbb{R}^n)$ and $\int_{B(0,1)} u_j dx = 0$, does $\{u_j\}$ converge in $L^p_{\text{loc}}(\mathbb{R}^n)$?

Published on 28 Mar 2026 - 1:26

score 168 · Answer 9 · 2026-03-25 11:04:51

168

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Let $T(f):=\frac{1}{x}\int_{0}^{x}{f(t)\,\mathrm{d}t}$ (the Hardy operator) find the norm of $T$ on $L^p$

Published on 25 Mar 2026 - 11:04

score 585 · Answer 10 · 2026-04-14 15:25:39

585

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Uniform convergence of a sequence of functions given as product and convolution.

Published on 14 Apr 2026 - 15:25

score 120 · Answer 11 · 2026-04-11 22:07:53

120

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Show that the following is a bounded linear operator on $L^2(R_+)$ Calculate the adjoint operator.

Published on 11 Apr 2026 - 22:07

score 67 · Answer 12 · 2026-04-16 10:38:46

67

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If $f \in L^1([a, 1])$ for all $a \in (0, 1)$, is it true that $f \in L^1((0, 1])$?

Published on 16 Apr 2026 - 10:38

score 1.4k · Answer 13 · 2026-04-15 07:32:51

1.4k

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Polynomials dense in $L^{2}(\mathbb{R})$?

Published on 15 Apr 2026 - 7:32

score 646 · Answer 14 · 2026-04-16 15:38:17

646

Views

Non-convergent Cauchy sequence in $\ell^1$ with respect to the $\ell^2$ norm

Published on 16 Apr 2026 - 15:38

score 224 · Answer 15 · 2026-03-26 22:19:58

224

Views

Inequality for Lévy SDE

Published on 26 Mar 2026 - 22:19

List Question

Minimizing an integral -- Hilbert space

Is it true that $\lim\limits_{r \rightarrow 1}f(r x) = f(x)$ in $L^1$?

Spaces of functions similar to $L^p$ but with different local and global sizes

Intuitive explanation of $L^2$-norm

Is it natural how $L^p$ spaces measure local and global sizes the same?

Subspace of $L^1(\Omega)$ closed

Properties of sequences of bounded functions in $L^2$

If $\{\nabla u_j\}$ is Cauchy in $L^p(\mathbb{R}^n)$ and $\int_{B(0,1)} u_j dx = 0$, does $\{u_j\}$ converge in $L^p_{\text{loc}}(\mathbb{R}^n)$?

Let $T(f):=\frac{1}{x}\int_{0}^{x}{f(t)\,\mathrm{d}t}$ (the Hardy operator) find the norm of $T$ on $L^p$

Uniform convergence of a sequence of functions given as product and convolution.

Show that the following is a bounded linear operator on $L^2(R_+)$ Calculate the adjoint operator.

If $f \in L^1([a, 1])$ for all $a \in (0, 1)$, is it true that $f \in L^1((0, 1])$?

Polynomials dense in $L^{2}(\mathbb{R})$?

Non-convergent Cauchy sequence in $\ell^1$ with respect to the $\ell^2$ norm

Inequality for Lévy SDE

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