Many of our market research databases provide companies/brands market share within their respective industry.  Try looking in:

• Passport
  Provides market share for a variety of consumer products.
• Statista
  Enter "market share" and the product or brand of interest to locate statistics from a range of sources.
• ​IBISWorld
  In each industry report, go to Major Companies tab.  The top industry players will be listed, along with their market share.

For historic market share information:

Market Share Reporter 
Ref. HF 5415.3 .M35 in the Stamps Reading Room.
Annual publication providing previously published market share data on companies, products, facilities, and brands. Baker's holdings go back to 1991.