How can I get the context in a fragment?

You can use getActivity(), which returns the activity associated with a fragment. The activity is a context (since Activity extends Context).

You can also override the onAttach method of fragment:

public static class DummySectionFragment extends Fragment{
...
    @Override
    public void onAttach(Activity activity) {
        super.onAttach(activity);
        DBHelper = new DatabaseHelper(activity);
    }
}