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  • 18 votes cast
Apr
24
awarded  Notable Question
Apr
23
accepted About $L^{p}$ norms and the Hilbert transform
Apr
23
comment About $L^{p}$ norms and the Hilbert transform
Thanks for your answer. Let me just ask a couple of things more: how does the $\sigma$-finite property of the Lebesgue measure imply that I can use the characterization? Is there any reference where I can read the proof? Second, okay, let us restric the domain of $H$ to $\mathcal{S}(\mathbb{R})$. Can I restrict the supremum to all functions $g\in\mathcal{S}(\mathbb{R})$ with $L^{p^{\prime}}$ norm $\leq 1$? I can prove that this is true if I know previously that $Hf$ is in $L^{p}$.
Apr
23
asked About $L^{p}$ norms and the Hilbert transform
Feb
28
awarded  Nice Question
Jul
21
asked Absolute continuity via maximal operator
Jun
1
accepted About convergence in norm of the Fourier Transform
May
31
comment About convergence in norm of the Fourier Transform
Why does the convergence holds for $g$ in the Schwartz class?
May
29
comment About convergence in norm of the Fourier Transform
Yes, but the convergence here is in norm. I don't see how this solves... :(
May
25
asked About convergence in norm of the Fourier Transform
May
7
revised An entire function that must be a polynomial
added 15 characters in body
May
7
revised An entire function that must be a polynomial
deleted 1 character in body
May
7
comment An entire function that must be a polynomial
I edited the question with the definition that I'm using :)
May
7
revised An entire function that must be a polynomial
added 214 characters in body
May
7
awarded  Informed
May
7
comment An entire function that must be a polynomial
But every function of exponential type zero would have to be constant, which is not true because any polynomial is of exponential type zero.
May
7
asked An entire function that must be a polynomial
Apr
20
awarded  Nice Question
Apr
12
comment Estimating an integral using the Poisson summation formula
It's $\sum_{|m| \leq j}f(m)$ in the end, right?
Apr
11
accepted Estimating an integral using the Poisson summation formula