Basically, Roberts Esnault-Pelterie's main contributions to space exploration and impact on society is
1) published two books called Astronautics in 1930 and Complement in 1934
which you can say he inspired later scientists and astronauts to explore space and expanded our understanding in space exploration and rocket science.
2) experimented with different liquid fuels in rocket motors of his design, including liquid oxygen and gasoline, and nitrogen peroxide and benzene, and then liquid oxygen and tetranitromethane
-as modern rocket engines often run on liquid fuels, his experiments with different fuel combinations can be said to expand our understanding of combinations that works and those that don't work at all,
3)in 1913, Peleterie calculated the energy required to reach the Moon and nearby planets
-assisted future exploration of these areas, these are essential scientific data needed to actually fly to these planets and moon, considered the first moon landing in 1969
4)proposed the use of atomic energy and nuclear power for interplanetary flight
-stimulated the minds of later scientists of other possible fuels and combination that could enable spaceships to explore the outer edges of our solar systems
He probably did not continue the work of a particular scientist, but rather he is very likely to be inspired as well as inspired the other four scientist in the syllabus, for example, Hermann Oberth won the Robert Esnault-Pelterie-Andre Hirsch Prize for his book Ways to Spaceflight which he proposed the idea of ion and electric repulsion rocket engines-so he obviously in various extent has been influenced by Pelterie's fourth main idea. Pelterie made significant contributions in the area of aviation, but that is not exactly a direct impact on space exploration. Hence I haven't included here. However, if you could like further information, check out these websites,
http://www.nmspacemuseum.org/halloffame/detail.php?id=7,
http://astronauticsnow.com/history/esnault-pelterie/index.html for more details. Hope this helped