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For the extreme case (p=1/(1+beta)), a weak estimate is given.
Instead of the boundedness in the extreme case, a weak estimate for ([b,H]) is showed.
In general, the ((H^{p},L^{q})) boundedness of ([b,H]) fails for (p=1/(1+bethen, then we give a weak estimate instead.
The authors prove the commutator ([b,H]) is bounded from (L^{p}(mathbb {R}^{n},dmu)) to (L^{q}(mathbb{R}^{n},dmu)) for (1< p<1/betandand from (H^{p}_{mathcal{F}}(mathbb{R}^{n})) to (L^{q}(mathbb{R}^{n},dmu )) for (1/(1+beta)< pleq1) and give the weak estimate at the extreme case (p=1/(1+betas) as well, which may give us an essential tool to study the linear or non-linear Monge-Ampère equation.
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"Although Q2 earnings are still likely to be weak, estimates have come down materially and now appear more in line with reality.
Item 1 is distant from both the mean level of difficulty of the items and the mean of the subjects, which confirms its "weak" estimates obtained from the three-parameter logistic model.
In the latter case, cosψ achieves its maximum (=1) interior to the interval ( ψ 1, ψ 2 ), and the indicated procedure yields instead the slightly weaker estimate ( sin ψ 2 − sin ψ 1 ) 2 4 B − 2 ( 1 − cos ψ 2 ) < B U 0 2 < ( sin ψ 2 − sin ψ 1 ) 2 4 B. (5.2b).
Our somewhat weaker estimate of this association relative to others [ 32] may reflect our shorter follow-up time, choice of comparison (reference) group and more functionally impaired sample.
Conversely, the results show that the MTS criterion provides weaker estimates compared to the MS criterion.
The JMA assessed Sarah to have been somewhat weaker, estimating peak ten-minute sustained winds of 150 km/h (90 mph) along with a barometric pressure of 950 mbar (hPa; 28.05 inHg).
This temporal analysis suffers from the difficulty of the likely weaker estimates of the eye movement measurements during the hazard sequence because they only make up a smaller percentage of the film sequence.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com