According to Bede, the Angles and Jutes which invaded Britain during the 5th Century came from an area roughly analogous to modern day Jutland and Schleswig. In the 8th Century, this same area is populated by the Viking Dane culture. If Bede is to be believed, it follows that there should be evidence of a Jutish or Anglo-Jutish culture remaining in the region and ultimately giving way, in some fashion, to the culture of the Danes.
Obviously it's best to take Bede with a pinch of salt, so my question ultimately is whether any such evidence exists in the historical or archaeological record and, if so, what light does it shine on the emergence of the Viking culture as the dominant culture of the Jutland Peninsula?
The culture that became the people we know as Anglo-Saxons did not arise wholly from continental antecedents in Northern Europe. While our Medieval sources, such as Bede, claim that the tribes that conquered what became England all derived from modern Denmark, northern Germany, and the Low Countries this is a gross oversimplification. In actuality the people that eventually coalesced into an Anglo-Saxon identity came from all over Northern Europe and the British isles, including native Britons, Romans, Irish, Picts, Welsh, Norwegians, Swedes, Danes, Jutes, Angles, Saxons, Frisians, Geats, and so on. Now in each of these places the majority of the population did not pull up stakes and set off to new lands, and the remaining people developed differently.
We shouldnt imagine the Jutes, assuming that there even actually ever existed a single Jutish identity, as "giving way" to a new Norse culture in Denmark. Rather it makes more sense that Nordic peoples living in Denmark contributed to the development of Anglo-Saxon identity once they immigrated to Britannia and the remaining population eventually was incorporated into Danish culture, there need not be an assumed mastery or dominion by one over the other. Whether these people self identified as Jutes is not really clear, but Denmark following the end of Late Antiquity started to coalesce into more centralized kingdom long before the rest of Scandinavia did.