Notation Question Regarding Integral Kernels Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Problem understanding proof for positive solutions of parabolic PDE in Friedman's textbookQuestion on how to prove sup(A) = sup(B) = sup(C)Determine where the function is continuousNorm of multiplication operator in $ell^2(Bbb N)$ is $|x|_infty$.Question about the proof that the sequence $a_jcdot b_j$ converges to $alpha beta $$H^s$ boundedness and $L^2$ convergence imply limit is $H^s$ boundedD. Williams 'Probability with Martingales' querySuppose $f$ is continuous on R such that $lim_hto 0 fracf(x+h)-f(x-h)h = 0$ for all $xinmathbb R$. Prove that $f$ is constant.Proving an open subset of $mathbbR^2$Clarification on Some Notation in a Lemma: Approximating LSC functions by Lipschitz continuous functions
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Notation Question Regarding Integral Kernels
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Problem understanding proof for positive solutions of parabolic PDE in Friedman's textbookQuestion on how to prove sup(A) = sup(B) = sup(C)Determine where the function is continuousNorm of multiplication operator in $ell^2(Bbb N)$ is $|x|_infty$.Question about the proof that the sequence $a_jcdot b_j$ converges to $alpha beta $$H^s$ boundedness and $L^2$ convergence imply limit is $H^s$ boundedD. Williams 'Probability with Martingales' querySuppose $f$ is continuous on R such that $lim_hto 0 fracf(x+h)-f(x-h)h = 0$ for all $xinmathbb R$. Prove that $f$ is constant.Proving an open subset of $mathbbR^2$Clarification on Some Notation in a Lemma: Approximating LSC functions by Lipschitz continuous functions
$begingroup$
I'm reading a proof of an estimate on an integral kernel. They sponateously introduce notation and I'm having trouble following what's happening. (The offending reference is the bottom of pg 60, Lemma A.14 here)
Let $f in L^1(mathbbR^N)$ and define:
$$Kf(x) = int_mathbbR^N fracf(y)x-y,dy quad forall xin mathbbR^N$$
They proceed with the following brief computation:
$$|K^epsilonf(x)| leq epsilon^1-N|f|_L^1 = epsilon^1-N$$
Thus
$$|K^epsilonf(x)| leq sigma/2 text where epsilon = (2/sigma)^1/(N-1)$$
Hence
$$textmeas > sigma leq textmeasK_epsilonf(x)$$
I'm having trouble understanding what $K_epsilon$ and $K^epsilon$ are. Any guesses?
real-analysis functional-analysis pde functional-inequalities
asked Mar 31 at 18:06
yoshiyoshi
1,261917
$endgroup$
add a comment |
$begingroup$
I'm reading a proof of an estimate on an integral kernel. They sponateously introduce notation and I'm having trouble following what's happening. (The offending reference is the bottom of pg 60, Lemma A.14 here)
Let $f in L^1(mathbbR^N)$ and define:
$$Kf(x) = int_mathbbR^N fracf(y)x-y,dy quad forall xin mathbbR^N$$
They proceed with the following brief computation:
$$|K^epsilonf(x)| leq epsilon^1-N|f|_L^1 = epsilon^1-N$$
Thus
$$|K^epsilonf(x)| leq sigma/2 text where epsilon = (2/sigma)^1/(N-1)$$
Hence
$$textmeas > sigma leq textmeasK_epsilonf(x)$$
I'm having trouble understanding what $K_epsilon$ and $K^epsilon$ are. Any guesses?
real-analysis functional-analysis pde functional-inequalities
asked Mar 31 at 18:06
yoshiyoshi
1,261917
$endgroup$
add a comment |
$begingroup$
I'm reading a proof of an estimate on an integral kernel. They sponateously introduce notation and I'm having trouble following what's happening. (The offending reference is the bottom of pg 60, Lemma A.14 here)
Let $f in L^1(mathbbR^N)$ and define:
$$Kf(x) = int_mathbbR^N fracf(y)x-y,dy quad forall xin mathbbR^N$$
They proceed with the following brief computation:
$$|K^epsilonf(x)| leq epsilon^1-N|f|_L^1 = epsilon^1-N$$
Thus
$$|K^epsilonf(x)| leq sigma/2 text where epsilon = (2/sigma)^1/(N-1)$$
Hence
$$textmeas > sigma leq textmeasK_epsilonf(x)$$
I'm having trouble understanding what $K_epsilon$ and $K^epsilon$ are. Any guesses?
real-analysis functional-analysis pde functional-inequalities
asked Mar 31 at 18:06
yoshiyoshi
1,261917
$endgroup$
I'm reading a proof of an estimate on an integral kernel. They sponateously introduce notation and I'm having trouble following what's happening. (The offending reference is the bottom of pg 60, Lemma A.14 here)
Let $f in L^1(mathbbR^N)$ and define:
$$Kf(x) = int_mathbbR^N fracf(y)x-y,dy quad forall xin mathbbR^N$$
They proceed with the following brief computation:
$$|K^epsilonf(x)| leq epsilon^1-N|f|_L^1 = epsilon^1-N$$
Thus
$$|K^epsilonf(x)| leq sigma/2 text where epsilon = (2/sigma)^1/(N-1)$$
Hence
$$textmeas > sigma leq textmeasK_epsilonf(x)$$
I'm having trouble understanding what $K_epsilon$ and $K^epsilon$ are. Any guesses?
real-analysis functional-analysis pde functional-inequalities
real-analysis functional-analysis pde functional-inequalities
asked Mar 31 at 18:06
yoshiyoshi
1,261917
asked Mar 31 at 18:06
yoshiyoshi
1,261917
asked Mar 31 at 18:06
yoshiyoshi
1,261917
asked Mar 31 at 18:06
yoshiyoshi
1,261917
asked Mar 31 at 18:06
yoshiyoshi
1,261917
1,261917
add a comment |
add a comment |
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