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 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 $L^{p}$. 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 7 comment An entire function that must be a polynomial I edited the question with the definition that I'm using :) 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. Apr 12 comment Estimating an integral using the Poisson summation formula It's $\sum_{|m| \leq j}f(m)$ in the end, right? Mar 15 comment About a generalization of the Riemann-Lebesgue lemma I've edited the question. Mar 15 comment About a generalization of the Riemann-Lebesgue lemma PhoemueX, I'm sorry, you're right. I'm trying to replace my first assumption. Yes, it turns out that the Lebesgue differentiation theorem solves the problem. g belongs to $L^1_{loc}$ then, when we take the limit, $g(x)$ will be bounded by M. I can just replace the two assumptions and the result will still hold :) thanks! Feb 15 comment Hilbert-Schmidt norm/smooth manifolds Yes, sorry, I forgot to mention that. I'll edit the text. Sep 27 comment Surface orientation Yes, the bases are orthonormal. I corrected that :) Thanks. This problem can be found on Montiel, Curves and Surfaces, page 76. Sep 3 comment About scalar products on $\mathbb{R}^n$ Done! :) Thanks May 29 comment Nilpotent operator / Orthogonal projection You're right, this isn't true under the given conditions. Oct 15 comment Representation of $S^{3}$ as the union of two solid tori Thanks, I edited the title and the tag :) Oct 4 comment Second countable topological space Thank you, Brian. =] Sep 18 comment Smooth Manifolds Thanks, Matt. I corrected it. Sep 12 comment Local Isomorphism on Topological Groups I've changed :) Sep 12 comment Local Isomorphism on Topological Groups Oh, sorry, I didn't make it clear. When I started to write this post I first put the title of the topic. He talks about generators of a group later in the same topic. Aug 19 comment Matrix subsets dimension Sorry, I've put three "n²-1". Actually, there are just two. I didn't understand it too, but this is how it is written =/ May 16 comment Basis to a manifold by coordinate balls Is S really contained in B (line 6)? You meant S contained in the image of B via (phi), no? May 14 comment Basis to a manifold by coordinate balls I forgot to ask something else... I have to show that there is a coordinate ball in S^n whose closure is equal to all S^n. The open ball of radius 1 is what we're looking for, isn't?