Complex sentence: The "Luftwaffe" lacked an effective air defence system early in the war, and as such, defending against the relatively sparse Allied daylight actions over German-controlled territory in 1939--1940 became the responsibility of the "Luftgaukommandos" (air district commands).
Split into simpler sentences: The "Luftwaffe" lacked an effective air defence system early in the war. The responsibility of the defence of German air space fell to the "Luftgaukommandos" (air district commands).