MHB Solving for $Mf \notin L^1(\mathbb{R})$ with $f \in L^1 (\mathbb{R})$

  • Thread starter Thread starter mathmari
  • Start date Start date
mathmari
Gold Member
MHB
Messages
4,984
Reaction score
7
Hello! :o

How can we find a $f \in L^1 (\mathbb{R})$ such taht $Mf \notin L^1 ( \mathbb{R})$, where $Mf$ is the maximum function ?? (Wondering)
 
Physics news on Phys.org
What is the maximum function?
 

Similar threads

I Why is this function not ##L^1(\mathbb{R} \times \mathbb{R})##?
  • · Replies 6 ·
Replies
6
Views
3K
I A concise "proof" of the Riemann-Lebesgue lemma
  • · Replies 1 ·
Replies
1
Views
2K
I Continuity of linear map from subspace of Euclidean space
  • · Replies 2 ·
Replies
2
Views
1K
I Norm of integral less than or equal to integral of norm of function
  • · Replies 3 ·
Replies
3
Views
2K
MHB Weierstrass Function: Continuous and Bounded on $\mathbb{R}$
  • · Replies 38 ·
2
Replies
38
Views
4K
I Uniform convergence of difference quotient in higher dimensions
  • · Replies 1 ·
Replies
1
Views
2K
I Discrete Subrings of Complex Numbers: Topology of Rings
  • · Replies 11 ·
Replies
11
Views
3K
I Does ##\mathbb{S}^1## embed in ##\mathbb{R}##?
  • · Replies 12 ·
Replies
12
Views
2K
MHB Proving Convexity of $f: \mathbb{R} \to \mathbb{R}$
  • · Replies 1 ·
Replies
1
Views
2K
B Is the Quotient Topology of Real Numbers Homeomorphic to Real Numbers?
  • · Replies 6 ·
Replies
6
Views
3K