Source: Bramoullé, David (2018), "Itinerant Objects in the Fatimid World: From Cairo to al-Andalus to Sicily and Back" Melikian-Chirvani, Assadullah Souren, (ed.), "The World of the Fatimids", p. 247 (map entitled "Extent of Fatimid Empire, ca. 1000 CE.")

Note: the cited source doesn't explicitly identify the territories as Zirid or Kalbid, but as "territories under Fatimid influence", as opposed to "under direct control". From context, it should be clear and transparent that these refer to the Zirids and Kalbids at this time. The Zirids were to lose control of Tripolitania very shortly after 1000 (but would also retake some of these territories on some occasions over the following decades), so this illustrates their presumed territory immediately prior to this. Here are some examples of reliable sources that provide context, if needed:

• "Zīrids", "Kalbids", and "Buluggīn (in Arabic: Buluḳḳīn) b. Zīrī" articles (various authors, 1960–2007), in Bearman, P.; Bianquis, Th.; Bosworth, C.E.; van Donzel, E.; Heinrichs, W.P. (eds.). "Encyclopaedia of Islam, Second Edition." Brill.
• Abun-Nasr, Jamil (1987), "A history of the Maghrib in the Islamic period." Cambridge University Press. (see Chapter 2, [1])
• Granara, William (2006), "Sicily", in Meri, Josef W. (ed.), "Medieval Islamic Civilization: An Encyclopedia". Routledge.([2])
• Brett, Michael (2015), "The diplomacy of empire: Fatimids and Zirids, 990—1062" in Bulletin of the School of Oriental and African Studies, vol 78, no. 1, pp. 149-159 ([3])