Question

Counterexample to $L^1$-boundedness of the maximal operator $f \mapsto f^\#$ with $f^{\sharp}(x):=\sup_{Q\ni x}\frac{1}{|Q|}\int_{Q}|f-(f)_{Q}|dy$

score 516 · Answer 1 · 2026-04-11 21:59:43

516

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Counterexample to $L^1$-boundedness of the maximal operator $f \mapsto f^\#$ with $f^{\sharp}(x):=\sup_{Q\ni x}\frac{1}{|Q|}\int_{Q}|f-(f)_{Q}|dy$

Published on 11 Apr 2026 - 21:59

score 468 · Answer 2 · 2026-04-12 23:19:45

468

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If a subspace of $L^p\cap L^q$ is closed with respect to both norms, the norms are equivalent on this subspace

Published on 12 Apr 2026 - 23:19

score 277 · Answer 3 · 2026-04-12 23:13:55

277

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Coordinate projections in $l^p$ are Lipschitz continuous

Published on 12 Apr 2026 - 23:13

score 214 · Answer 4 · 2026-04-09 05:18:08

214

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About completeness of complex exponential systems

Published on 09 Apr 2026 - 5:18

score 391 · Answer 5 · 2026-03-18 23:57:19

391

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Find the number of interior points of this subspace of $l^2$.

Published on 18 Mar 2026 - 23:57

score 127 · Answer 6 · 2015-10-16 15:52:43

127

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A function $f$ that is not in any $L^p$ but the measure of $\{|f|>t\}$ is bounded by $C/t$

Published on 16 Oct 2015 - 15:52

score 31 · Answer 7 · 2026-04-02 16:54:21

31

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$ ( \int_{\mathbb R}[\int_{\mathbb R} |f(x,y)|^{p} dx]^{p/q} dy)^{1/q} < \infty$ for large $N$?

Published on 02 Apr 2026 - 16:54

score 3.2k · Answer 8 · 2026-03-31 19:04:02

3.2k

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$f \in L^p \cap L^q$ implies $f \in L^r$ for $p\leq r \leq q$.

Published on 31 Mar 2026 - 19:04

score 1.5k · Answer 9 · 2026-03-26 12:38:43

1.5k

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Exercise 4 chapter 7 Evans book

Published on 26 Mar 2026 - 12:38

score 1k · Answer 10 · 2015-10-18 20:34:31

1k

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$L^q(X) \subset L^p(X)$ if $p\leq q$ and $\mu(X) < \infty$.

Published on 18 Oct 2015 - 20:34

score 1.1k · Answer 11 · 2026-04-03 21:45:22

1.1k

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The containment between the Schwartz space, its dual, and the Lebesgue space $L^2$

Published on 03 Apr 2026 - 21:45

score 824 · Answer 12 · 2026-04-13 01:08:25

824

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Completeness of the sum of two $L^p $ spaces

Published on 13 Apr 2026 - 1:08

score 4k · Answer 13 · 2026-04-16 07:50:15

4k

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$ l^1$ not reflexive

Published on 16 Apr 2026 - 7:50

score 4.9k · Answer 14 · 2026-04-11 18:04:38

4.9k

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Convergence in $L^1$ norm, but not point-wise a.e.

Published on 11 Apr 2026 - 18:04

score 84 · Answer 15 · 2015-10-21 00:00:00

84

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Growth rate of $g(p)=\int_0^1\log(-\log(x/e))^p\,dx$ and similar functions

Published on 21 Oct 2015 - 0:00

List Question

Counterexample to $L^1$-boundedness of the maximal operator $f \mapsto f^\#$ with $f^{\sharp}(x):=\sup_{Q\ni x}\frac{1}{|Q|}\int_{Q}|f-(f)_{Q}|dy$

If a subspace of $L^p\cap L^q$ is closed with respect to both norms, the norms are equivalent on this subspace

Coordinate projections in $l^p$ are Lipschitz continuous

About completeness of complex exponential systems

Find the number of interior points of this subspace of $l^2$.

A function $f$ that is not in any $L^p$ but the measure of $\{|f|>t\}$ is bounded by $C/t$

$ ( \int_{\mathbb R}[\int_{\mathbb R} |f(x,y)|^{p} dx]^{p/q} dy)^{1/q} < \infty$ for large $N$?

$f \in L^p \cap L^q$ implies $f \in L^r$ for $p\leq r \leq q$.

Exercise 4 chapter 7 Evans book

$L^q(X) \subset L^p(X)$ if $p\leq q$ and $\mu(X) < \infty$.

The containment between the Schwartz space, its dual, and the Lebesgue space $L^2$

Completeness of the sum of two $L^p $ spaces

$ l^1$ not reflexive

Convergence in $L^1$ norm, but not point-wise a.e.

Growth rate of $g(p)=\int_0^1\log(-\log(x/e))^p\,dx$ and similar functions

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