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From dyadic $Lambda_{alpha}$ to $Lambda_{alpha}$

من لامبدا الدايادية إلى لامبدا $\alpha$

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 Added by Alberto Torchinsky
 Publication date 2007
  fields
and research's language is English




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In this paper we show how to compute the $Lambda_{alpha}$ norm, $alphage 0$, using the dyadic grid. This result is a consequence of the description of the Hardy spaces $H^p(R^N)$ in terms of dyadic and special atoms.



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We present in this paper some embeddings of various dyadic martingale Hardy-amalgam spaces $H^S_{p,q},,, H^s_{p,q},,,H^*_{p,q},,,mathcal{Q}_{p,q}$ and $mathcal{P}_{p,q}$ of the real line. In the same settings, we characterize the dual of $H^s_{p,q}$ for large $p$ and $q$. We also introduce a Garsia-type space $mathcal{G}_{p,q}$ and characterize its dual space.
We study the singly-Cabibbo-suppressed decays $Lambda_c^{+}to peta$ and $Lambda_{c}^{+}to ppi^{0}$ using $Lambda_{c}^{+}Lambda_{c}^{+}$ pairs produced by $e^+e^-$ collisions at a center-of-mass energy of $sqrt{s} = 4.6; GeV$. The data sample was collected by the BESIII detector at the BEPCII collider and corresponds to an integrated luminosity of 567 $pb^{-1}$. We find the first evidence for the decay $Lambda_{c}^{+}to p eta$ with a statistical significance of $4.2sigma$ and measure its branching fraction to be $mathcal{B}(Lambda_c^+to peta)= (1.24pm0.28({rm{stat.}})pm0.10({rm{syst.}}))times10^{-3}$. No significant $Lambda_c^+ to ppi^0$ signal is observed. We set an upper limit on its branching fraction $mathcal{B}(Lambda_c^+ to ppi^{0}) < 2.7 times 10^{-4}$ at the 90% confidence level.
The ratios of the branching fractions of the decays $Lambda_{c}^{+} rightarrow p pi^{-} pi^{+}$, $Lambda_{c}^{+} rightarrow p K^{-} K^{+}$, and $Lambda_{c}^{+} rightarrow p pi^{-} K^{+}$ with respect to the Cabibbo-favoured $Lambda_{c}^{+} rightarrow p K^{-} pi^{+}$ decay are measured using proton-proton collision data collected with the LHCb experiment at a 7 TeV centre-of-mass energy and corresponding to an integrated luminosity of 1.0 fb$^{-1}$: begin{align*} frac{mathcal{B}(Lambda_{c}^{+} rightarrow p pi^{-} pi^{+})}{mathcal{B}(Lambda_{c}^{+} rightarrow p K^{-} pi^{+})} & = (7.44 pm 0.08 pm 0.18),%, frac{mathcal{B}(Lambda_{c}^{+} rightarrow p K^{-} K^{+})}{mathcal{B}(Lambda_{c}^{+} rightarrow p K^{-} pi^{+})} &= (1.70 pm 0.03 pm 0.03),%, frac{mathcal{B}(Lambda_{c}^{+} rightarrow p pi^{-} K^{+})}{mathcal{B}(Lambda_{c}^{+} rightarrow p K^{-} pi^{+})} & = (0.165 pm 0.015 pm 0.005 ),%, end{align*} where the uncertainties are statistical and systematic, respectively. These results are the most precise measurements of these quantities to date. When multiplied by the world-average value for $mathcal{B}(Lambda_{c}^{+} rightarrow p K^{-} pi^{+})$, the corresponding branching fractions are begin{align*} mathcal{B}(Lambda_{c}^{+} rightarrow p pi^{-} pi^{+}) &= (4.72 pm 0.05 pm 0.11 pm 0.25) times 10^{-3}, mathcal{B}(Lambda_{c}^{+} rightarrow p K^{-} K^{+}) &= (1.08 pm 0.02 pm 0.02 pm 0.06) times 10^{-3}, mathcal{B}(Lambda_{c}^{+} rightarrow p pi^{-} K^{+}) &= (1.04 pm 0.09 pm 0.03 pm 0.05) times 10^{-4}, end{align*} where the final uncertainty is due to $mathcal{B}(Lambda_{c}^{+} rightarrow p K^{-} pi^{+})$.
Let $mathcal{H}_{alpha}=Delta-(alpha-1)|x|^{alpha}$ be an $[1,infty) ialpha$-Hermite operator for the hydrogen atom located at the origin in $mathbb R^d$. In this paper, we are motivated by the classical case $alpha=1$ to investigate the space of functions with $alpha$-{it Hermite Bounded Variation} and its functional capacity and geometrical perimeter.
A search for the flavor-changing neutral-current decay $Lambda_{c}^{+} to pmu^+mu^-$ is reported using a data set corresponding to an integrated luminosity of $3.0rm fb^{-1}$ collected by the LHCb collaboration. No significant signal is observed outside of the dimuon mass regions around the $phi$ and $omega$ resonances and an upper limit is placed on the branching fraction of $mathcal{B} (Lambda_{c}^{+} to pmu^+mu^-) < 7.7~(9.6)times 10^{-8}~{rm at}~90%~(95%)$ confidence level. A significant signal is observed in the $omega$ dimuon mass region for the first time.
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