The Schireson Brothers, (Jack and Nat), were a music retailer and distributor in Los Angeles, CA. I don't have a detailed history of Schireson, but this is what I do know. They were founded in 1902 and they sold all sorts of instruments not just Ukuleles. They patented a kind of steel cone resonator and went to court with John Dopyera over it in the 30's; a case they lost in 1937, (apparently their resonators were not as effective as Dubros anyway but he still had most of them destroyed so now they are very rare). 

In addition to branding other people's instruments like the big Chicago and New York distributors, (Globe was the main Chicago supplier, and they also distributed Samuel Osborn and Hawaiian Mahogany products too), they did actually manufactured their own, in fact in the 1920's they were the only US company making the Mexican range of folk instruments, (plus they had local luthiers like the original Delgado Guitars make instrument for them).

Hollywood, (with the red diagonal stripe across the headstock though this may have changed in later years), was the main brand name for their instruments and this was used on Mandolins and Guitars as well as Ukuleles and Banjoleles. There were 10 styles of Ukulele in their catalogue (well I have seen 8, 9 and 10 with 10 being the best so I assume there were 10?) and most, but not all of the Ukuleles were what is now Concert scale.

Mai Kai was another of their brands, (and this I believe was only used on Ukuleles) and they did put their own name, (Schireson), on some instruments too.

Lyric and Perfect are other brand names I have seen used in Schireson Bros. sound hole labels