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Akira
  • Member for 8 years, 2 months
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revised
Does Gaussian heat kernel ensure $\int_{\mathbb R^d} (1+|x|) \sqrt{\ell_{t_0} (x)} \, \mathrm d x < \infty$?
added 5 characters in body; edited title
revised
Does Gaussian heat kernel ensure $\int_{\mathbb R^d} (1+|x|) \sqrt{\ell_{t_0} (x)} \, \mathrm d x < \infty$?
edited title
awarded
 Cleanup
comment
Does Gaussian heat kernel ensure $\int_{\mathbb R^d} (1+|x|) \sqrt{\ell_{t_0} (x)} \, \mathrm d x < \infty$?
@gmvh I made an edit at the same time as yours, which may be the reason...
revised
Does Gaussian heat kernel ensure $\int_{\mathbb R^d} (1+|x|) \sqrt{\ell_{t_0} (x)} \, \mathrm d x < \infty$?
edited title
revised
Does Gaussian heat kernel ensure $\int_{\mathbb R^d} (1+|x|) \sqrt{\ell_{t_0} (x)} \, \mathrm d x < \infty$?
rolled back to a previous revision
asked
Does Gaussian heat kernel ensure $\int_{\mathbb R^d} (1+|x|) \sqrt{\ell_{t_0} (x)} \, \mathrm d x < \infty$?
comment
Does $\int_{\mathbb R^d} (1+|x|^{1 + \alpha}) \ell (x) \, d x < \infty$ imply $\int_{\mathbb R^d} (1+|x|) |\ell (x)|^{1-\alpha} \, d x < \infty$?
Thank you very much for your informative answer.
comment
Comonotone solution for Optimal Transport problems with supermodular surplus
For the sake of clarity, please add the definitions of "supermodular" and "comonotone".
accepted
Does $\int_{\mathbb R^d} (1+|x|^{1 + \alpha}) \ell (x) \, d x < \infty$ imply $\int_{\mathbb R^d} (1+|x|) |\ell (x)|^{1-\alpha} \, d x < \infty$?
accepted
Rate of convergence of mollified functions in $L^p$ norm
asked
Does $\int_{\mathbb R^d} (1+|x|^{1 + \alpha}) \ell (x) \, d x < \infty$ imply $\int_{\mathbb R^d} (1+|x|) |\ell (x)|^{1-\alpha} \, d x < \infty$?
comment
Convergence of mollified functions in weighted $L^p$ norm
Ah I got it. Thank you for your informative answer. Are you aware of results about convergence rate of this kind?
comment
Convergence of mollified functions in weighted $L^p$ norm
Our goal is to bound $\int \left| \int \rho_n(x-y) f(y) dy - f(x) \right|^p d\mu(x)$, but your treatment is about $\int \left| \int \rho_n(x-y) f(y) dy \right|^p d\mu(x)$. Could you elaborate more?
accepted
Convergence of mollified functions in weighted $L^p$ norm
comment
Rate of convergence of mollified functions in $L^p$ norm
@AymanMoussa I am aware of your question, but functions of my concern are not necessarily (weakly) differentiable.
revised
Rate of convergence of mollified functions in $L^p$ norm
deleted 7 characters in body
revised
Convergence of mollified functions in weighted $L^p$ norm
deleted 2 characters in body; edited tags
asked
Rate of convergence of mollified functions in $L^p$ norm
asked
Convergence of mollified functions in weighted $L^p$ norm
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