Narrow coverage at wide-angle isn't unusual, though, and some of the corner darkening is likely from the lens itself ... though the Sony RX100 raised ISO to 320 to achieve that.
Sample Photos - The Sony ... lens at the wide-angle setting. At the telephoto end of the lens, it's close enough to allow for some pleasing background blur/bokeh. ISO Noise Performance - The RX100 ...
f/5.6 The Sony RX100 is equipped with ... but coverage is not centered and the lens casts a strong shadow in the lower right. You'll likely want to use external lighting for the closest RX100 ...