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Akira
  • Member for 8 years, 2 months
  • Last seen this week
  • Japan
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revised
Is the difference between $\alpha$-Hölder constants of $f*\rho$ and $g*\rho$ controlled by $\|f-g\|_\infty$?
added 43 characters in body
asked
Is the difference between $\alpha$-Hölder constants of $f*\rho$ and $g*\rho$ controlled by $\|f-g\|_\infty$?
revised
Lipschitz approximation of a probability measure with finite $1$-st moment by the ones with finite $p$-th moment
edited tags
asked
Lipschitz approximation of a probability measure with finite $1$-st moment by the ones with finite $p$-th moment
comment
Let $\mu : [0, T] \to \mathcal P_2^a (\mathbb R^d), t \mapsto \mu_t$ be absolutely continuous. Is $t \mapsto \mathcal H (\mu_t)$ continuous?
Thank you very much for taking time to write such a detailed answer!
accepted
Let $\mu : [0, T] \to \mathcal P_2^a (\mathbb R^d), t \mapsto \mu_t$ be absolutely continuous. Is $t \mapsto \mathcal H (\mu_t)$ continuous?
comment
Does $f(t) \le \int_0^t (t-s)^{-\frac{1}{2}} [f(s) + |f(s)|^{\beta}] \, \mathrm d s$ imply $f=0$?
I am sad that it is not true but thank you so much for your answer!
accepted
Does $f(t) \le \int_0^t (t-s)^{-\frac{1}{2}} [f(s) + |f(s)|^{\beta}] \, \mathrm d s$ imply $f=0$?
revised
Does $f(t) \le \int_0^t (t-s)^{-\frac{1}{2}} [f(s) + |f(s)|^{\beta}] \, \mathrm d s$ imply $f=0$?
deleted 183 characters in body; edited title
asked
Does $f(t) \le \int_0^t (t-s)^{-\frac{1}{2}} [f(s) + |f(s)|^{\beta}] \, \mathrm d s$ imply $f=0$?
accepted
Grönwall-type inequality for $f(t) \le \alpha + \int_0^t (t-s)^{-\frac{1}{2}} [f(s) + |f(s)|^{\beta}] \, \mathrm d s$
comment
Grönwall-type inequality for $f(t) \le \alpha + \int_0^t (t-s)^{-\frac{1}{2}} [f(s) + |f(s)|^{\beta}] \, \mathrm d s$
Thank you for your answer! I wonder if we can obtain a tight upper bound in the sense that if $\alpha=0$ then $f=0$.
asked
Grönwall-type inequality for $f(t) \le \alpha + \int_0^t (t-s)^{-\frac{1}{2}} [f(s) + |f(s)|^{\beta}] \, \mathrm d s$
awarded
 Fanatic
accepted
Decay rate of $\lim_{|z| \to \infty} \|1_{B(z, 1)} f\|_{L^p} =0$
comment
Decay rate of $\lim_{|z| \to \infty} \|1_{B(z, 1)} f\|_{L^p} =0$
I am sorry for being sloppy. I meant the inequality to be satisfied for all $f \in L^{p+\delta} (\mathbb R^d)$ and $z \in \mathbb R^d$...
revised
Decay rate of $\lim_{|z| \to \infty} \|1_{B(z, 1)} f\|_{L^p} =0$
added 19 characters in body
asked
Decay rate of $\lim_{|z| \to \infty} \|1_{B(z, 1)} f\|_{L^p} =0$
reviewed
Approve
Decay estimate of moment of an SDE
accepted
Decay estimate of moment of an SDE
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