Abstract The elliptic flow$$(v_2)$$ of$${\textrm{D}}^{0}$$ mesons from beauty-hadron decays (non-prompt$${\textrm{D}}^{0})$$ was measured in midcentral (30–50%) Pb–Pb collisions at a centre-of-mass energy per nucleon pair$$\sqrt{s_{\textrm{NN}}} = 5.02$$ TeV with the ALICE detector at the LHC. The$${\textrm{D}}^{0}$$ mesons were reconstructed at midrapidity$$(|y|<0.8)$$ from their hadronic decay$$\mathrm {D^0 \rightarrow K^-\uppi ^+}$$ , in the transverse momentum interval$$2< p_{\textrm{T}} < 12$$ GeV/c. The result indicates a positive$$v_2$$ for non-prompt$${{\textrm{D}}^{0}}$$ mesons with a significance of 2.7$$\sigma $$ . The non-prompt$${{\textrm{D}}^{0}}$$ -meson$$v_2$$ is lower than that of prompt non-strange D mesons with 3.2$$\sigma $$ significance in$$2< p_\textrm{T} < 8~\textrm{GeV}/c$$ , and compatible with the$$v_2$$ of beauty-decay electrons. Theoretical calculations of beauty-quark transport in a hydrodynamically expanding medium describe the measurement within uncertainties.
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Multipliers on bi-parameter Haar system Hardy spaces
Abstract Let$$(h_I)$$ denote the standard Haar system on [0, 1], indexed by$$I\in \mathcal {D}$$ , the set of dyadic intervals and$$h_I\otimes h_J$$ denote the tensor product$$(s,t)\mapsto h_I(s) h_J(t)$$ ,$$I,J\in \mathcal {D}$$ . We consider a class of two-parameter function spaces which are completions of the linear span$$\mathcal {V}(\delta ^2)$$ of$$h_I\otimes h_J$$ ,$$I,J\in \mathcal {D}$$ . This class contains all the spaces of the formX(Y), whereXandYare either the Lebesgue spaces$$L^p[0,1]$$ or the Hardy spaces$$H^p[0,1]$$ ,$$1\le p < \infty $$ . We say that$$D:X(Y)\rightarrow X(Y)$$ is a Haar multiplier if$$D(h_I\otimes h_J) = d_{I,J} h_I\otimes h_J$$ , where$$d_{I,J}\in \mathbb {R}$$ , and ask which more elementary operators factor throughD. A decisive role is played by theCapon projection$$\mathcal {C}:\mathcal {V}(\delta ^2)\rightarrow \mathcal {V}(\delta ^2)$$ given by$$\mathcal {C} h_I\otimes h_J = h_I\otimes h_J$$ if$$|I|\le |J|$$ , and$$\mathcal {C} h_I\otimes h_J = 0$$ if$$|I| > |J|$$ , as our main result highlights: Given any bounded Haar multiplier$$D:X(Y)\rightarrow X(Y)$$ , there exist$$\lambda ,\mu \in \mathbb {R}$$ such that$$\begin{aligned} \lambda \mathcal {C} + \mu ({{\,\textrm{Id}\,}}-\mathcal {C})\text { approximately 1-projectionally factors through }D, \end{aligned}$$ i.e., for all$$\eta > 0$$ , there exist bounded operatorsA, Bso thatABis the identity operator$${{\,\textrm{Id}\,}}$$ ,$$\Vert A\Vert \cdot \Vert B\Vert = 1$$ and$$\Vert \lambda \mathcal {C} + \mu ({{\,\textrm{Id}\,}}-\mathcal {C}) - ADB\Vert < \eta $$ . Additionally, if$$\mathcal {C}$$ is unbounded onX(Y), then$$\lambda = \mu $$ and then$${{\,\textrm{Id}\,}}$$ either factors throughDor$${{\,\textrm{Id}\,}}-D$$ .
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- Award ID(s):
- 2349322
- PAR ID:
- 10509669
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Mathematische Annalen
- Volume:
- 390
- Issue:
- 4
- ISSN:
- 0025-5831
- Format(s):
- Medium: X Size: p. 5669-5752
- Size(s):
- p. 5669-5752
- Sponsoring Org:
- National Science Foundation
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